>Are there any studies that show [immigration] would help growth?

Immigration increases wages for domestic workers in the long-run[1-3].

"None of these studies is decisive, but taken together they suggest that immigration, in the long run, has had only a small negative effect on the pay of America's least skilled and even that is arguable. If Congress wants to reduce wage inequality, building border walls is a bad way of going about it." http://www.economist.com/node/6771382 and here http://www.economist.com/blogs/freeexchange/2013/10/immigrat....

[1] http://www.nber.org/papers/w12497 [2] http://www.nber.org/papers/w14188 [3] http://www.hamiltonproject.org/papers/what_immigration_means