This will be the greatest thing that could happen to Odovacer, though he doesn't know it of course.
I doubt it would definitely have changed something in Italy, at least when it comes to Gothic invasion. It looks more as an inner conflict of the extended Thracian dynasty rather than a strong disagreement on foreign policy.
At this point, Goths (from Pannonia, Danube and Thracia) were already quite a pain for northern Roman regions, so giving them some motivation to go in Italy would probably be the logical choice for Zeno's successors. Admittedly, it could be delayed if they're enrolled to fight in an harsh succession war, and Theodoric Strabo would certainly have a far better deal ITTL (especially without Hunnic attacks), especially if he's related to the PoD (Thracian Goths comes earlier, and manages to help Marcian).
But, giving the facility both Theodoric had to agree when it came to general Gothic interests, they would represent a clear threat.
Either it means that Theodoric Strabo manages to hold a kingdom within Romania, either it means a more divided Gothic side in Italy with one of both Theodorics suddenly and mysteriously dying at some point.