I'm a plumber and work with PVC pipe almost daily. The glue is designed to work with the primer. Not all primer is purple, they do make clear stuff. The reason why it is purple so that inspectors can see it has been primed and so that you can remember what you have primed and what you haven't.
The glue will hold with out the primer though. The primer is pretty nasty stuff so try not to get it on your skin, and don't huff the fumes from the can cause you'll get a nasty headache.
With that being said, if you're just using the piping in the tank and underwater, I wouldn't bother gluing or priming anything. Dry fit usually holds pretty well. I've even come across joints in houses that someone forgot to glue and have held for years. If the piping is outside of the tank I would absolutely prime and glue it to prevent leaks onto a floor.
I have a PVC spray bar in my tank and it's dry fit, not glued.