I guess the Stargate must have some sort of effect on the cloaking device because even when they go through a space gate cloaked they come back through decloaked.
You would probably still notice a cloaked vessel exiting the Stargate either in the displacement of the wormhole as it exits of the ripples along its surface. The Wraith would then know that a cloaked puddle jumper is around and probably then send darts to patrol for the jumper.
They always wait until they've existed the Gate then cloak the Jumper (on the other side I mean). And as Hermiod pointed out if they Gate home cloaked it comes out decloaked the other side anyway. The wormhole must not allow the cloak to function.