Yes, body armour is warn under the jersey. I assume you are referring to "body armour" suit type setups...with chest, elbow, shoulder pads and all in one shirt like format? What Jeff is referring to is a different setup I believe, more like an under jersey chest (only) protector, with no arms or spine protection.
I don't wear the armour myself, but have a buddy with it. It is a little warmer than a traditional chest protector, but not too bad (doesn't bother him any, but we're not in the desert either). Great protection though, and most importantly spine protection.