Not necessarily if all restaurants are forced to raise prices at the same time. And when low income people have more pocket money, they tend to spend it, potentially at all these restaurants, providing a stimulus of sorts. I would happily pay $0.55 more for a burger.

All markets have boundaries. You could say an "open market" for meat would allow supermarkets to sell grade D meat to shoppers without labelling it. Or that anybody can practice medicine without a license. It's perfectly reasonable to define the market for labor to exclude most immigrants in order to protect the investment young engineers make in their educations. On the flip side, you could just allow any and all immigrants into the country. Where will you house the 2 billion people from China and India?