As a small amount of data, my asking salary has never been less than the highest paid H1B at a company plus another $30k/yr, and I've always been offered more than I've asked, despite the H1B position being more senior. That doesn't prove wages being dragged down by itself, but it's evidence of H1B workers being paid less than the legally mandated "actual wage", and ECON 101 can take care of the rest in terms of the expected effects on the market.