Yes, but this requires planning beforehand, and should not be installed as an afterthought, because the system may not function well, and in worse-case scenarios it can ruin your floor finish.
The easiest floor finishes to include with a floor heating system are hard – such as polished concrete, stone, or tiles.
This is because they are good conductors – and if unheated, they are dead cold.
Carpet, timber and other thermal resistive floor finishes aren’t as obvious when heated – but they still make all the difference in the room (between having a cold uninviting room and a naturally warm and comfortable feeling room).
Euroheat has successfully been installing floor heating under all floor finishes in Australia for almost thirty years.