I would like to think that if you have a sturdy cage and don't leave the cham loose unattended with the cat around, you should probably be fine. But remember that they can and will break/rip screen if they want to.
I am lucky in that none of my cats are really interested in my little critters (rats and hamster) in their cages. One of the cats will sit there and watch them sometimes, but gets bored fairly quickly. The same one I've found sitting in front of the cham cage, but I'm pretty sure it's just because of the heat lamp, as my cham barely moves.