Yep, that's what happens - it pools.
Modern standards in many G20 countries require new (and rennovating) houses in radon prone areas to provide appropriate ventilation.
Geographically in also pools in still valleys, often during the night and morning with radon 'clouds' clearing from the floor by afternoon (as can be seen when processing airborne radiometric survey data and applying radon removal filtering to normalise U-Y-Th maps).