The salaries paid to skilled US tech workers in the tech hubs without unions are already so much higher than anywhere else in the world, even after adjusting for cost of living, that I don't see the impact happening the way you say it. The workers who have skills and experience would unionize at some tech workplaces so that they don't have to job hop for fair treatment, but in any case they already make more in the US than elsewhere, because employers know they have to go to the US tech hubs to have a high concentration of great tech workers, and unions wouldn't change this. (I know there are many great tech workers elsewhere, but not nearly as concentrated.)
Most of the high-skilled tech hubs I'm aware of outside the US are in countries with stronger worker protections than the US, and often more unionization too. (This does vary, absolutely - worker rights are greater in Berlin or Paris than they are in Zurich or London.)
Now, for low-paid low-skilled workers, the situation might be different, but those aren't determinative of where a tech company is based long-term, and the union would be best if it spans all skill levels.
Unions aren't just a US thing, by the way. Hello from Quebec where unions are far more common than anywhere in the US. Even undergraduate university students are typically unionized here, complete with strikes and cross-university federations with elected leadership. Much of Europe is also far more unionized than the US, though certainly not the part of it you referenced by Eastern Europe (maybe aside from Finland).