No freaking shit it does. When I was working at OSU as a research assistant in the materials engineering depertment when several of the American students graduated in that department they we're offered entry level positions at around $60,000/year (this was in the mid 90's). Several of the Asian students were' made offers to when they graduated. According to their student visa's they had six months after graduating to find a US job or they would have to return home. Considering starting pay for an entry level engineering job in India, China, SE Asia was around $500 to $800/month they were take any reasonable job offers. So they were getting offers of around $30,000 to $35,000 per year which indeed does drive down the wages in the tech market.
I've seen the same happen in Nursing. Wages for RN's went down dramatically in the 2000's as compared to the 1990's due to a huge influx of nurses immigrating to the US.