Comment by SpicyLemonZest

An offshored worker is already much cheaper than an H1B worker, I would expect any easy substitutions along those lines to already be performed. Probably some effect on the margins, but I would doubt it outweighs the primary effect.

(Of course, it would be a problem if you think H1Bs are for hiring people who cannot be found domestically, but it does not seem like many people think that these days.)