If you don't put the pressure sensors in the new wheels the low pressure light will come on. You can transfer the sensors to the new wheels, but have to be very carefull about getting a good seal on them. You may have to get new O ring seals; the originals may be too small for the stem holes in the new wheels.
I put new wheels on my Armada last week. I didn't want to bother with getting the wheel pressure sensors moved over. The first time I drove the car on the freeway, the light turned on. Then the light turned off and has stayed off and nothing has changed.
Since my new wheels are still 70 series tires, I'm not too worried about the air pressure. I visually look everyday at the tires to make sure they are inflated and if they look low, I'll fill them up.
If you are getting 20-24" wheels, you probably want to move the sensors over because on low profile tires, you can't afford to let the pressure get low.
It's not hard to do. Unless your wheels don't have the correct size hole cut for the sensor screws, rubber seals, and clearance for the sensor on the inside.
Most wheel shops will move the sensors over and rebalance the wheels for around $80.
Andy, that is good to know about the TPM. I thought perhaps that the sensors only sent a signal when the pressure was low, but I was talking to a wheel guy today and he seemed to think that when they are moving they send a signal periodically even if the pressure is not low. That syncs up with what you are saying in that the first time the system was looking for a sensor reading. Perhaps the programmers were smart enough to figure if they are not getting any readings from any corner that maybe the stock wheels & TPMs were removed!
I have been thinking about getting 20's and leaving the TPM on the stock wheels to add dedicated snows onto (studded, if someone will make them). So, any how with 20's you can still run a 50 or 60 series tire (305/50 20 or a 275/60 20 or ...) so you just have to check tire pressure manually like I have for the last 25 years!