..for example will my tire pressure system show that I have an error?

yes the symbol will stay on the dash, unless you buy sensors in the tire valves to mimic the sensors of the stock wheels. The sensors should be available by now to purchase. If not deal with the light on like i have, because the sensors werent avail yet wen i bought my wheels.

You could've used the sensors on your old wheels

You could've used the sensors on your old wheels
they dont fit.

i'm gonna be running multiple sets of wheels for autox, track, winter, street, etc. on my car when I buy one. I'm just going to deal with that silly TPMS light when I'm not using the stock RFTs (which suck btw).

I take it there's no loss of power when the TPMS light comes on?

Nope

I take it there's no loss of power when the TPMS light comes on?
Are you serious?