First of all, no this is not normal. No, a blocked roof vent will not stop the gray water from draining. It might drain more slowly, but it will drain. It could conceivably suck a trap dry, but that is not likely, but it will drain.
As already suggested, it is not uncommon for trash to be allowed to drop into the tank when the openings for the fitting are drilled and my guess would be you have debris which moves around when the tank is holding water.
If that is the case, there is no good way to remove it without cutting into the tank and if the debris is larger than the tank outlet the problem will recur.
Put enough water in the tank so you are sure it should drain (I went on a service call one time where the owner was sure there was a problem and there was almost nothing in the tank to drain). Then if it doesn't drain, again as suggested already, run a tape up through the valve, you can't hurt anything doing that. If you are lucky, maybe the debris is comprised of multiple small pieces and might break free. That would give you bath in gray water, but a working gray water valve.
Otherwise, if the problem persists you will have to access the tank and replace it or cut an access opening into it and then seal the opening (no good options here).