Yes, it would *work* but not the way you want it to. You are not considering the principle of radiant heat.
The PEX with hot water running though them heats the surrounding cementitious material and after a spell continues to radiate the heat into the room. Radiant heat if different than the other forms of heat you are probably more familiar with.
When the PEX is embedded inside the concrete it is effectively inside a conduit, just like regular PVC water piping is. If the pipe breaks, so what?, its inside another pipe made of concrete.
When PEX is installed on a 2nd floor that is constructed of wood it is secured to the wood subfloor with the proper channels and then a layer of light weight concrete is poured over top, again, embedding the PEX inside the concrete.
If you want to heat the air in a room a $20 space heater will do that, but when it cycles off the air quickly cools. If you want to heat the room and the things in the room that is where radiant heat shows its stuff.
And then there's electric radiant floor heat but thats a whole nuther animal.