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The BCM can only read four sensors at one time; therefore, it is programmed from the factory to read the four sensors on the ground, and it will disregard the sensor in the spare.
Since the system used on the H3 does not display the location of a specific sensor if there is a problem with the tire's pressure, you do NOT need to relearn the sensors after the rotation, if you only rotate the four tires on the ground.
However, if you decide to rotate all five tires (four on the ground and the spare), you must (well, you should) relearn the sensors since the BCM will be reading three sensors on the ground, plus the tire that became the spare. Meanwhile, what used to be the spare will not be read, until you relearn.
When you set the system into the relearn mode, the sensors retained in memory are erased. So, when you lower the pressure in each tire to allow the BCM to relearn, it will honk to notify you when each sensor is learned, up to four sensors. (The lowering of the air pressure in the tire causes the sensor to wake up and send out a signal. The dealers use a special tool that when held near the tire's valve stem (the valve stem is part of the sensor), makes the sensor send out a signal to allow the BCM to learn that particular sensor.)

If you switch tires and rims when going off-road, I would say live without the sensors, just make sure your tire pressure is ok before traveling on the road. Your TPM will go off each time you run through an ignition cycle (off/on), and the message will be displayed (unless you hit the button). If you decide to put sensors in the off-road tires, you would then have to go through the relearn each time you put the tires on and then again when switching back, plus if you airdown, you have have the TPM message.
Just my opinion, but if it was me, and I was just going to run one set while off-roading, I would not purchase extra sensors. Sensors are available via GM service parts.