Well this is heat transfer... not thermodynamics (but close enough for layman discussions!). Radiation is certainly always happening. The question is whether it is a significant part of the heat transfer away from the person sleeping in the tent. The equation is:

q" = epsilon*sigma*T^4

Epsilon is a number between 0 and 1 and it is what you are changing by using a reflective surface.

Sigma is the Stefan-Boltzman constant and is a really small number (5.67 x10^-8 W/m^2-K^4) and it means that radiation heat transfer is negligible unless temperature differences are really large. Notice the temperature is raised to the 4th power!

Radiation heat transfer travels through line of sight, so the most important thing you need to do is block your line of sight to space (which is really, really cold). That is why a tent wall keeps you quite a bit warmer. Your tent wall will be near atmospheric temperatures (instead of space temperature). Your sleeping bag will be a bit warmer than outside temps but not significantly so there won't be much radiation heat transfer between the two bodies.

Bill's Bakers tent works well with a reflective surface because he uses it with a high temperature heat source (fire). The reflective surfaces give more line of sight paths for radiation heat transfer to occur over.

hope that helps