What happens if I use Sudden Disappearance?
No, his creatures will not have summoning sickness. He will control them continuously since the beginning of his turn.


  302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.