Assuming that all the unskilled labor is in competition with each other.
What if there are really two markets: one in unskilled citizen labor and
one in unskilled undocumented labor. Of course there is some relation.
I would assume we want to get rid of the market in unskilled
undocumented labor, at least to the degree that it depends on the fact
that these workers have no rights.
It's true that more workers drive down the price; but I would thing that
the main engine is the lack of rights. The employers are not hiring
undocumented workers because there's a labor shortage. If the currently
rightless workers were allowed to organize, I would think that would
drive wages up, and that this would outweigh any effect due to an
increase in immigration resulted from the increase in rights.
As for emigration hurting the source countries, I would think this would
only concern us in the case of "raiding" or "brain drain", not in the
case of unskilled workers. Some would argue that would-be unskilled
migrants should be kept penned in their home countries to foment unrest
there, but I don't think you're so merciless - ;)
-bob naiman