Yes, do NOT drive the Jeep without the skid plate installed - not even a short test drive. When removing the skid plate, the proper practice would be to support the trans/t-case with a jackstand on the bell-housing of the trans. Then you can safely remove the skid plate and add another jack stand on the transmission mount you found.
Without your skid, the entire weight of the trans/t-case is resting on six bolts that hold the trans to the motor. If you drive it like that, your driveshaft angles will likely be horrible causing possible damage to the t-case/shaft/diff - not to mention what a small bump could do to the six bolts holding everything together.
Check out this writeup
for changing trans and t-case fluids. In order to change the t-case fluid properly, you need to drop the skid, so it covers all the steps there.