The company can't deport/revoke every single H1B's visa if a wide scale move is made to unionize them.
Why haven't unions tried calling corporate bluffs and tried unionizing H1B's? Seems like a century ago, unions would've gone to the ends of the earth to be the representation for underpaid immigrants.
You might be visualizing desperate street urchins ousting tottering older Americans. From what I observed the IT workers being Rifd are quite skilled, having bubbled up from mergers. Many H1Bs appear to come from higher class families so they might be more interested in Management positions in some cases. I hope that helps. There is a lot of information online and the book Sold Out covers the topic very well.
I think it's worth trying. Otherwise, organized labor has truly forgotten its roots and no longer gives a damn about the exploited immigrant worker.
I think it would have as much success as a cowboy holding out a handful of hay in the middle of a cattle stampede.
Everyone afraid to touch this subject?