Welllllll... considering that Dante was (albeit with considerable nuance) defending the position of the Emperor vis-à-vis the Pope, there are avenues for his work to gain traction. His theological views being adopted as true by a break-off group of faithful is possible. If they also accept his De Monarchia as the correct view of the investiture controversy, it is possible that the complex political situation of the time (interregnum without a Holy Roman Emperor being crowned; subsequent avignon Papacy) can end up bolstering just such a pro-imperal sect.
Suppose that instead of Henry VII being crowned Emperor (the first in a long time) by Pope Clement V (the first Avignon Pope), the rise of the "Dante sect" leads to an ATL claimant to the imperial title who uses the establishment of the Avignon Papacy as "proof" that the Seat of Saint Peter is vacant, proclaims himself Emperor, declares the theological and legal beliefs of Dante to be the correct ones, and claims that it is his mission to restore the true Papacy. (By which he means: to install his own preferred candidate in Rome, based on the understanding that as of now, the Pope will no longer have any temporal authority, and the primacy of temporal power in all Christendom lies with the Holy Roman Emperor.)
It's not the most likely scenario, but I can see it happening.