the short answer is that bringing in skilled labour will usually increase aggregate demand, because these are people that end up with spending money that is recycled back into the economy. you actually want to talk about multiplier effects, not wage suppression.

however, bringing in unskilled labour will generally have minimal effects, as they are paid so poorly as to only be able to subsist, if they aren't sending their excess wages out of the country. if they aren't occupying jobs that domestic workers can do directly, they are at least setting the wage floor much lower than it otherwise would be.

it would follow that you would want to put a focus on skilled immigration to plug holes in labour demand, while insisting that labour laws for unskilled labour are strictly upheld, to prevent employers from taking advantage of immigrant labour.