I've been aware of Ludwig Viktor's homosexuality since before I devised the plan of four thrones for four sons. He would take the Polish Throne at the age of 6 and I've acted under the impression that sexual orientation is not something that can be altered or butterflied away. That said, I feel it very likely that in a scenario where Ludwig Viktor is King of Galicia/Poland that Sophie would drill into his head the importance of creating a Polish Line. She likely would do this to all of her sons. As a result Ludwig Viktor might take a wife and establish a royal line for the sake of Dynasty. In the event that he doesn't there is now plenty of precedent for the Habsburgs to force him to abdicate in favor of one of his cousins' lines (probably Karl Stephan). I don't see the Habsburgs allowing any of their thrones to pass out of the family, after all they fought the War of Spanish Succession basically over dynastic rights In any case, it makes for an interesting story to be told as part of the AH.I just became aware that adult Ludwig Viktor had ahem character foibles (very public homosexuality and transvestitism) that shall be rather embarassing for the Habsburg once he's put in the very public status of a monarch and shall create a dynastic crisis in the long term (he could not even muster the effort to pick a beard wife and sire some children like most gay nobles typically did, and Franz Joseph eventually forbade him to stay in Vienna). When he becomes adult, he shall probably have to be goaded into abdication and be replaced by another Habsburg (or perhaps by a Hohenzollern-Sigmaringen).
As for the creation of a TL, to be blunt I would prefer that the idea of 4 Thrones for the 4 Sons of Franz Karl and Sophie be left for me to flesh out someday in a TL. That said obviously I can't forbid anyone from developing it (as I see someone's already started), those are just my feelings on the subject. I would not be reading or available for comment on any such TLs because I do genuinely want to write it out someday and would not want cross contamination to occur (I fear Eurofed has already influenced me too much )