If there were no illegals doing work for cheap, then yes average salaries would go up... but they would go up for everyone thus balance would be restored.
Illegals working for less off the books is only an issue when some businesses use them and others don't giving those that do an unfair advantage since they can then undercut their competitors on price.
But if it was nearly impossible to hire illegals... then every business would be in the same boat and would just adjust the price of their cost of goods or services accordingly.