[jeff5may]

Yes it does! In your case especially, the radiant energy is low-grade, long-wave, far infrared heat. Unless we are in a vacuum, there is matter in the air whose atoms will be heated by this radiation. Extra water vapor in the air acts as a sponge for infrared. The further the journey, the more heat is lost along the way. Even if 1/2 of 1 percent of the radiated heat goes into the air, you are still setting up eddy currents within the air. The other 99.5 percent that may or may not make it to a far surface is heating your crawl space by all 3 mechanisms from the bottom and sides.

In this situation, you are heating your whole crawl space with the heat loss through the bottom of your floor. The radiated energy that is not drained away by the walls and ground is causing the convective heating of your crawl space that you ignore.

Lets compare no insulation to 4 inches of insulation below your floor.

With no insulation, and with your "warm-air-buoyancy" acting as a gradient layer of resistance to conduction and convection within this 4 inches at a value of Q=0.5 BTU/SqFt per hour per DegF, at a delta t of 30 DegF, this layer would lose heat at a rate of 1500 BTU per hour per 100 square feet to the crawl space below it. At the boundary of your floor joists, the air drops 5 degF and nature takes its course from there. Somewhere in the middle of the crawl space, the air has a mean value of 17.5 degrees below floor temp.

With the 4" of insulation, lets say it cut that Q value to 0.05 and in that 4 inches, the temperature drops 22 degF. In this case, the layer would lose heat at only 150 BTU per hr per 100 SqFt downwards, the rest of which quickly heats the spaces in the floor between your heat pipes. Somewhere in the crawl space, the air has a mean value of 26 degrees below your floor temp.

More importantly, the insulation trapping and spreading this lost heat around gives the upper surface of the floor more effective means to heat the space above it.