Not necessarily true..... On my 2000, the honeycomb all broke free and was actually blowing to the exit and blocking my exhaust flow to the point of having almost no power under throttle. I took mine off, and cleaned out the housing, then put the bare housing back on the exhaust.
My 2000 did not have an O2 sensor after the cat (neither does my 2001) so the computer has no way of telling if I have a cat or not. Nothing is measured (in this configuration) beyond the pre-cats at the exhaust manifold.
We argued to great lengths on the Colorado4x4 board about weather or not a 4.0 without a cat will pass emissions or not. There were ton of people who said there was no way.
Here in Colorado, we are emissions tested on a Dyno up to about 60mph. My emissions were low enough that I had a fast pass (extremely low emissions enough to pass without finishing the whole test). Also, having the Cat housing made sure you passed the visual inspection for emissions components.
This is my experience, and it may differ for other people. (but it is first hand experience, not I heard a friend of a friend of a friend that burned up his engine because he took his cat off)
Now, if you have a system that has an 02 sensor after the cat, ignore what I've said. The computer will be able to tell, and the CEL will probably come on.