So while it would take some time to see the results, and the casual factors probably not be put down to immigrants leaving (or being denied/not applying to enter the US to begin with), you would see an eventual impact on job creation and economic growth.
Perhaps the slow recovery after the 2007 crisis could be partially put down to the post-9/11 paranoia and making it more difficult for smart people to enter the US? It's total speculation on my part (something that occurred to me as I typed this comment), but an interesting idea nonetheless.
Also, the Economist published a list of best countries to be born in: http://www.economist.com/news/21566430-where-be-born-2013-lo...
The US is 16th, behind Australia, Canada, and many European countries. Years ago America was on top.