When there's big profit to be made, maybe! I've traveled all across this country and you'd have to be blind not to see who is doing the heavy lifting from east to west.
As per my name, I live up north where we don't have many immigrants yet alone illegal ones. But during a snowstorm with 20 mph winds, I see Americans in buckets next to telephone polls restoring electricity. I see them in -0 temperatures in boots standing in two feet of water digging up water lines to repair the busted ones. I see Americans on those steel beams 20 stories high walking across them like most of us walk through a park. I see Americans all over joining our military for a pittance of money we pay them, just so they can earn benefits once they leave.
The problem here is that yes, companies seek the most profit. However, if they are forced to increase their offer for employment, that's how wages increase in our country. If you bring in people who are willing to do these shit jobs for shit money, that doesn't happen.