No: A 20W tire is a 20W tire at 18 mph. At 10 mph, it's roughly a 10W tire (rolling resistance should be mostly linear at these speeds). Going from 20W to 10W tires therefore only saves you 10W total at those speeds.
At 120W, you are idle pedalling. You do not really pedal lighter, so saving a few watts mean an increase in speed, but as both rolling resistance and aerodynamic drag goes up with speed the gain becomes small.
At normal climbs - the time where you'd wish pedalling was easier - you're either 1. spend in the area of 200-300W maintaining the same speed without increasing rolling resistance, making rolling resistance a smaller part of the load, or 2. drop to a granny gear, going very slow to maintain your 120W and thus making the rolling resistance negligible with any tire. In either case, rolling resistance matters much less in climbs.
