Suppose I have a unit of assault Terminators on the board, and they are joined to a Librarian who has the Gate of Infinity power. Can he, in the movement step, use the power to deepstrike the squad, and then, in the assault step, can that squad assault as normal?
Gate of Infinity allows units to be placed as per the Deep Strike rules. According to the Deep Strike rules you cannot assault the same turn you arrive via Deep Strike. You are also subject to any other rules related to Deep Strike. You scatter, are affected by terrain, and can mishap the same as if you arrived via normal Deep Strike.
Here's an example forum thread where the general consensus is that you can't assault through a Gate of Infinity.