It does stack, but any other modifiers would still apply, and the stealth suit would only apply to sight perception tests. If against a critter with an improved sense of smell it wouldn't do anything. Or if they do something that makes noise (like shot a gun) it will give bonuses to the person trying to perceive them.
Stealth is an opposed test of their modified skill vs the observer's modified perception.
As far as astral space I believe that the spirit would be visible which in turn may draw attention to them unless they are also concealing themselves on the astral plane too. My opinion would be that this is two separate services.