The Haskalah wasn't entirely assimilationist, though, despite what the Hasidim would have you think

. It was in fact fairly religionist, with the assimilationism coming later. Maskilim - especially early Maskilim - were more concerned with a synthesis of Jewish and Enlightenment thought. Actually, the Yiddish revival itself is basically a Maskil movement.
Still, if we look at the Haskalah "proper", it starts more or less with Mendelssohn. He had a very traditional (and fairly poor) Jewish upbringing in a small city in Prussia, complete with yeshiva, where he was clearly the most brilliant student and was sort of adopted by the local rabbi as a likely successor. So far, so ordinary. That rabbi was, when Mendelssohn was 14 or 15, called to Berlin and brought the boy with him, where he became a mostly autodidactic polymath, and used his knowledge of Talmud and the heretical but still Judaism-based writings of Spinoza as a springboard into general Enlightenment philosophy, inhaling Locke, Descartes, Liebniz, etc. as well as the Classics. He wrote several essays in German and became convinced that Jews needed to learn the local language in order to flourish...but far from suggesting that they abandon their Judaism or anything like that, he translated the Torah into German to serve as a teaching tool for learned Jews who would no doubt be intimately familiar with the Torah's text! He never converted and as far as I can tell never considered converting, as many "modernizing" or "assimilationist" Jews did, and in fact famously refused to get into a pissing contest about Jesus' role in the context of Judaism.
Much of the early Haskalah was intensely focused on the Torah (and Prophets and Writings, too), with the emphasis on applying new Enlightenment thoughts and principals to interpretation of what was still the Supreme Book (well, Books), and the Biurists/Maskilim (more or less synonymous at the very beginning) were intensely insulted when reactionaries accused them of being heretics or atheists.
That said, these early Maskilim were definitely anti-Yiddish, as evidenced by their magnum opus - though it should be noted that commentary on the Torah was very seldom done in Yiddish, so in a way their commentary in German was more akin to the Reformation policy of translating the Bible into the common tongue [and not Hebrew] than it was a rejection of Yiddish; hypothetically, a translation of the Bible into Yiddish would have been right up their alley. The problem with that, though, is that at the time (and through today in many ways), Yiddish was an anti-prestige language. It was the language of ignorance and poverty, not like German [and Latin, and French], gateways to modern society and broader philosophy. Another problem is that thought Mendellsohn came from humble, Yiddish-speaking roots, most of the big early Maskilim were wealthy and German or Dutch speaking from the get-go, Court Jews of Vienna and Berlin or merchants from Amsterdam and London more than shtetl-dwellers.
But you know what? This revolutionary act of translation could, in theory, go the other way. Maybe not Mendelssohn, maybe not the OTL Maskilim, but maybe someone else in those circles thinks that the idea of opening Jews up to the greater world is great, but thinks that it will be too hard to teach that many people proper German, and decides instead of start translating other books from Latin and German and whatever into Yiddish. Maybe Leibniz and some German philosophers first, but eventually French, English, and of course the Latin and Greek classics (in fact, people have found contemporary translations of some of these into Hebrew, which could be translated into Yiddish). This could lead to a translation of the Torah into Yiddish, maybe, and begin a tradition of commentary in that language (very much paralleling the Christian Reformation in this sense).
There's no compelling reason such a movement couldn't start shortly after the "proper" Haskalah (say, about the same time as the American Revolution, well in time of the Napoleonic Wars). For comparison, this is about a century before OTL and would get it into the gate before Nationalism really starts up in Europe. Which will could have interesting implications I'll discuss a little below.
Vis. its reception, such a movement would probably be met with skepticism by the "mainstream" rebels, especially since OTL's Haskalah marked the start of Hebrew Revivalism, linked mostly to a personal understanding of the texts and commentaries (compare if the Christian Reformation had coupled translating the Bible into German with a push for ordinary citizens to learn Latin). Still, they were an eclectic bunch, and some folks might grab on to it, especially when it gets to the Russians out east, who were supposed to be a little looser than the Germans.
The bigger problem would be the traditionalists. OTL, the Jewish mainstream mostly hated the Maskilim (in fact, in many ways Orthodox Judaism in the modern day is a reaction to the Haskalah - though not Modern Orthodox Judaism

), but also mostly left them alone (at least, at first). They knew that while the movement might skim off some of the cream of Jewish society, the majority of Jews would not learn German regardless. As the Haskalah spread east, though, the reactions became much stronger, not least because the Mitnagdim and the Hasidim were already at each others' throats, and everyone was nervous because of the recent false messiah Yaakov Frank, who had rallied the residual followers of Shabtai Tzvi, and had as one of his main principals study of the Tanach itself in favor of the Talmud and Mishne (sound familiar?). OTL Mitnaged and Hasidi rabbis denounced the Haskalah and did everything they could to oppose it, while Russian Maskilim spent a lot of effort mocking the former groups. A Yiddish-speaking Haskalah would be even more dangerous here, and it might make much more significant headway than OTL's, which left lots of communities more or less untouched, especially in the rural parts of the Pale, which remained more or less the same between 1600 and 1900, and then often transplanted directly to New York or Bnei Brak with little fanfare. A Yiddish-speaking Haskalah, emphasizing reading the holy books in a language that everyone spoke well, and opening the gateways of commentary to each and every Jew, and in 1800, could have an effect on Polish and Russian Jewry that cannot possibly be overstated. Honestly, I can't even conceive what could happen. In fact, I have a suspicion that the Tsarist authorities would be fiercely against such a thing (though the Austrians would probably be pretty laissez-faire).
Returning to pre-Nationalism Yiddish: Jews struggled during the rise of nationalism in Europe. Basically the only Jews that were exposed to outside ideas were assimilated Jews or Maskilim, and the latter were often buoyed by a sort of Enlightenment "post-nationalism" (a horrible abuse, as it was before nationalism...) that all men were equal and brothers etc. OTL, the French Revolution and the accompanying emancipation of Jews put a lot of wind into the sail of Jewish assimilationism. Zionism would only emerge in the late-ish 19th century as a reaction to the steadfast refusal of European nationalists to accept Jews as being part of their nation. But if there was a strong-ish movement of Yiddish culture and philosophy at the time, then non-assimilationist Jewish thinkers might be a little stronger, and Jewish Nationalism might actually rise together with other nationalisms instead of later, as a reaction to rejection. This might even, very very hypothetically, lead to something like a Jewish contingent in the November Revolt, or a solely/primarily Jewish uprising against Russia or Austria (or Prussia, I guess, but Prussia was typically both less oppressive and easier to emigrate from). This might end up putting Jewish nationalism on an equal footing with Greek, Polish, Albanian, Serbian, etc nationalism in the European eye (though I doubt it...), which could hypothetically lead to a European attempt to carve out a Jewish state in the Pale (hypothetically, say, in a Versailles-type treaty, though this would no doubt butterfly WWI as OTL).
Such a movement would definitely have a strong effect on Zionism, though Zionism per se might still exist as you'll still have assimilationist Jews getting rejected. ITTL, they might turn to embrace Yiddish and the Pale instead of Hebrew and Palestine, though they might just as easily proceed as OTL anyway.
Thank you for your post, you've given me a lot to think about!