The President doesn't even have to impose restrictions - their entry is already illegal.
The question is what happens when they break the law and are apprehended and in US custody, and the law is pretty clear that they can request asylum.
From the same Act: "The president may, by proclamation and for such a period as he shall deem necessary, suspend the entry of all aliens or any class of aliens, immigrants or non- immigrants, or impose any restrictions on the entry of aliens he may deem to be appropriate."
Those requesting asylum are a class of immigrant.
FReegards!