Im taking out my catalytic converter on my 1986 IROC throttle body 305 there is a little gray pipe coming out of the middle of the cat and going up into the engine bay im wondering what it is and what i should do with it?

It is for the AIR (Air Injection Reaction) Pump. It's an engine driven air pump, that moves air through that tube and into the center of the converter.

Do you need to pass a visual emissions component inspection?

No we don't and we figured out its the smog pump do u have any tips as to how to delete that and what to do with the belts

Another thing would it be ok taking out the cat and leaving the pump running?

You can buy a "delete pully" or re-route your belt. There is a thread on the belt re-routing somewhere on here (thirdgen). I took mine out and used the delete pully keeping the original belt routing. About a $60 part. I also removed the smog plumbing from the manifolds and plugged the holes with brass plugs. As far as the cat goes, I cut off the smog pipe and welded it shut. You could probably plug it with something if you don't have access to a welder.

If I take the cat out but not the pump (I'll take the pump out eventually) can I just plug that hole and call it good for now?

The pump will seize if it isn't connected.