I think it will. For years, most of the illegal border crossers from Mexico were Mexicans or South Americans looking for work. There still are a huge number of them. We can stop those by making it impossible for them to get jobs here - and that won't happen unless the employers have a legal source of workers.
What it sounds like you're saying is that the illegal workers currently in the country, if legalized, will take up the jobs that foreigners from the south would be coming here for, and thus discourage them from coming. But if that's the case, then the illegals currently in the country would already be taking up those jobs. Making them legal won't change the economics of that situation.
Not at all. What I've been trying to say is that American employers need to have a way to make sure that their employees are legal (be they guest workers, immigrants or citizens), and that they have to be held responsible for hiring any who are not. Further, they should have a way to hire as many legal workers as they need.
The problem is not the illegals as much as it is employers who need workers, and can't find legal ones.