I don't know how the jeeps are, but i had to take the passenger seat out of my silverado once. It had a weight sensor under it, and was an automatic airbag. If there was no passenger, it wouldn't enable that airbag. I just took that one out and disconnected the sensor while no power was on no problem.
If I remember I got the airbag warning light in the dash cluster bacause the computer recognized that the sensor had been disconnected. But that was it.
Are you putting it back in, or is it going to be out for a while? Only problem I could see is the rest of the system maybe not working right while it is out. But if you are doing it with the ignition off and no power going to the computer, and plug everything back in before you start it up again there should be no issue. And just to be on the cautious side, disconnect the battery first.
I'm not sure how the JK's are made, but my TJ had no electrical stuff under the seat anyway. It just had a key switch for always on or always off, just in front of the shifter.