Well, if Hasdai ben Shaprut, de facto foreign minister of al-Andalus in the late 900s, was willing to travel across the Med and Black Sea to meet the king of the Khazars, imagine how many Jewish notables across Eurasia would come to meet this King David... It would probably rival the Hajj. And, assuming that crusade actually goes through a lot of these Jews may not be coming back home, and may be joined by many thousands more chased out by pogroms. But regrettable as that is, it
is a
return of the Jews to their homeland, so...
But after the initial excitement wears off, then the questions will pile up. The nomadic teachers who accompanied David the Turk south are going to have the best claim on positions in the new Temple's priesthood, which means they'll be assuming a lot of new authority at other Jewish leaders' expense-- and this is a massive and fractious group. Whether we're talking about village teachers in rural Yemen or cosmopolitan intellectuals like Maimonides, a
lot of people are going to be expected to legitimate these parvenu Davidians from the east, and lend them the authority and power needed to reconstitute the Jerusalem priesthood. Some rabbis may accept this, most may respond by challenging the validity of this new Messiah and the depth of his knowledge about Judaism. Best case, they ask to debate him and members of his court personally. Worst case, they raise a revolt to keep this "false messiah" from becoming a second Jesus. And the problem with winning Messianic authority by the sword is that if this Messiah starts to be defeated in the field by Muslim and Christian armies both...
Anyways, for a preliminary time frame--
- Conversion of the Khazar royals, by the Khazar king Joseph's account, happened around 740.
- Let's say Judaism takes the next century of so to filter through the lower-Volga population, with converted tribes added to the Genesis genealogy of humanity as explained in King Joseph's letter. This is actually a fairly interesting thing about Judaism-- the conception of humanity as a series of patrilineal clans that regard each other with generational friendship/enmity actually coincides pretty well with the Central-Asian herders' outlook on such matters. Among the Turkmen, Baloch, etc., groups would often claim to have a common ancestor as justification for sealing an alliance or establishing a federation (this study of Turkmenistan goes into more detail, p. 25 more specifically). So being added to the Genesis family tree ("Know that we are descended from Japhet, through his son Togarmah...") would allow a converted tribe to claim familial ties with (read: protection and friendship from) the royals and each other, which is probably as good an incentive as any for giving up pork and the whole circumcision business.
- The Khazar federation extends east, intercepting the Oghuz and Karluks fleeing the collapse of the Gokturk Khaganate. The idea of creating new federations along the Khazar model gains some appeal, Oghuz is recast as a "son of Togarmah". If the Karluks are converted too, then that prevents them from reforming into the Karakhanids (and likely saves Xinjiang Buddhism).
- Sviatopolk of the Kievan Rus destroys the Khazar state in the late 900s, but the area is quickly taken over by Cumans and Kipchaks as in OTL. Maybe some are willing to listen to the Jewish teachers wandering around. The locals begin to organize against Persian/Arab slave raids.
- *Eventually*, a local clan rises to paramount authority. The Japhetite origin of the Turks is revised slightly, allowing this clan to portray themselves as descendants of Shem-- more specifically, of David's line.
David's conquest could probably come in--
- 1040: in an alt-Dandanqan, the Oghuz King David and his Kipchak auxiliaries swat aside the Ghaznavids, and then run into the Abbasids and their Buyid protectors. David can't respond to this problem as the Seljuks did (usurping the Buyids as the Caliphate's protectors) so they're probably fighting their way through Mesopotamia too...
Problem is, since the Seljuk conquest of Jerusalem was what started the Crusades in the first place, David is pretty much going to be the primary target of this world's First Crusade. And while the Franks sail in from across the sea, the leftover Abbasids and rivals hoping to displace them scramble to solidify their reputations as "guardians of the holy places" by taking the Middle East back.
- mid-1100s: the Turkish-Jewish kingdom grows up under the protective umbrella of the Western Liao, takes the place of the Khwarezmians and fills the void left behind by the Seljuks' decline.
The conquest of Iran might end up being easier, but Saladin's Ayyubids won't be so easy to punch through. If David's lucky the Crusaders might see him as an anti-Muslim ally, but that probably ends the moment he starts rebuilding the Temple.
- Any time after this, the Mongols have redrawn the map of Asia and left behind big hulking khanates that are more likely to go Muslim than anything else.
***
TL;DR: The Messiah probably can't unite the world's Jews behind him for very long (if at all), and he'll have whole continents' worth of enemies.