Question about catalytic converters (temp)

I currently have BBK headers and BBK off road H-pipe on my car. However, I ran across a BBK X pipe with cats for $100, and decided to buy it. The current H-pipe I have has had the hangers (that go into the trans xmember) cut off, and it hangs down awfully low. I only put 200 miles since throwing that on and it's already annoying me. The question I have, is if it would be alright to put the X pipe on with the cats, even though I am not running the air pump. Would this create too much heat? I was told that some track day events at places like MAM, cats are not even allowed due to heat issues. Should I repair the H-pipe I have on the car? Or does not running an air pump even affect the temp of the X pipe at the cats? Thanks for any input.

I don't care whether the cats are actually functional though. I just was wondering if there would be a heat issue. Don't want any fires or something.

So I should not run the x pipe with cats without an air pump due to the exhaust clogging up. I will then find a better way to hang the H-pipe that no longer has the hangers for the crossmember. Does anyone by chance have any pointers for this? The car is basically used for track use, so it has to be quite secure.