Well, without half of it anyway. If defeated Prussia is likely to lose Silesia and its Rhenish Provinces at least - probably other bits as well. It will most likely be just a rump state on the Baltic.
I'm curious to see your reasoning for this. IOTL, Austria itself didn't suffer any territorial losses at all in the Austro-Prussian War; the Prussian leadership was worried about foreign intervention and ended the war quickly, rather than taking such a drastic step. Will the Austrian-led German Confederation
dare to so greatly weaken Prussia when Russia is still Prussia's ally? I doubt it.
It's actually even worse for Austria than that implies, because the Second French Empire, until Prussia's astonishing victories, expected Austria to win and wouldn't want its great enemy (as Austria
was until 1866) to become too powerful. Even if you make Prussia lose to Austria, there are not just one but
two other great powers that are likely to intervene on Prussia's side if Austria looks dangerously successful.
Bismarck went to war with Austria at a time that was extremely opportune to Prussia; whether or not anyone chooses to think it was deliberate on his part, I leave to their discretion.
In conclusion: Prussia decisively losing the Austro-Prussian War is a WI of questionable usefulness, since I don't think it could have actually happened; the best I can imagine Austria doing (even if Prussia's army is much weaker than IOTL) is advancing into Prussia, being forced to back down and perhaps taking some of Silesia or a few of Prussia's western territories in exchange for not being dogpiled by the rest of Europe.
Bismarck not becoming Minister President of Prussia could have preserved the German Confederation.
This is one of the cases where, I feel, popular opinion (largely correct) of Bismarck as a political genius translates falsely into "Great Man of History"-style attribution of large-scale historical forces to single men. (Apologies, by the way, for addressing this criticism and quoting only your own post, as it's not just you who've made claims like this.)
As Mikestone8 mentioned in a previous post, in OTL William I did want to attend the Congress of Frankfurt in 1863 but Bismarck prevented him from doing so. Let us say with a different Minister President in office, William does attend the Congress. William was having problems with the Landtag and was looking for help with his domestic situation. William would have probably asked for some concessions from Francis Joseph before accepting the Reform Act.
And this is where. What motivation does Prussia have to accept any loss of Prussian sovereignty to an organisation including, and led by, a great power that was Prussia's major rival? IOTL the Prussian leadership weren't pan-Germanist ideologues, they were pragmatists; they opposed pan-Germanism when it came as
Großdeutschland and supported it when it came as
Kleindeutschland, because Prussia wanted a Germany where, far from having to give up its own power to another hegemon, it would itself be hegemon, and that was difficult in any Germany including Austria.
Just because Wilhelm went to the Congress wouldn't mean he would agree to anything permanent. Indeed, I strongly suspect he wouldn't—unless we suppose one of his bursts of eccentricity (at one point late in the Austro-Prussian War he wanted to march all the way to Vienna rather than make peace).
Francis Joseph could have promised him military support against any domestic insurrection if Prussia accepted the Reform Act.
Given Austria's (well-proven) vulnerability to domestic insurrection in comparison to the considerably stabler Kingdom of Prussia, such a promise would be somewhere between an insult and a joke.
William may have asked that Austria and Prussia share the presidencies of both the Directory and the Bundesrat.
Any concession giving Prussia at least equality with Austria, if not outright superiority, would be demanded by Prussia and rejected by Austria, which saw itself as (and largely was) the leader of the German states until 1866.
William might insist on Prussia always sitting on any military committees and possibly negotiate a “constable” position over the federal army for the kings of Prussia in the event of war. Francis Joseph would not have given William everything he wanted but I believe he would have been able to convince William to approve the Reform Act.
This strikes me as "Great Man of History" thinking again. Prussian actions were determined by Prussian interests, and it was not in Prussia's interests to subsume itself under an Austrian-led greater Germany. Even if Wilhelm I himself approved it in one of his occasional bizarre impulsive bursts, the aristocratic Prussian reactionaries whom he tended to appoint to high office in government would rip any such thing to shreds, and OTL has proven (e.g. with the aforementioned example of the late Austro-Prussian War) that they were capable of restraining him in those bursts.
In TTL, Prussia and the other German states would not have supported Austria’s ambitions in Poland, Italy, or the Balkans, but Austria would have had the option of a more aggressive foreign policy without having to worry about a war against Prussia.
Yes, it's certainly in Austrian interests to neutralise Prussia as a threat to its hegemony over the German states and put Prussia into a greater Germany in which Austrian interests will largely hold sway. Prussia has no such incentive.