What's the right answer? Will it help?
I would tend to believe the first plumber in principle, although without a computational fluid dynamics analysis of the room scenario, I'd be skeptical of the "significantly improve" assertion. Most of the radiator installation literature I looked at had the radiator installed above the baseboard or ~3-6" off the floor with Runtal's instructions (http://www.runtalnorthamerica.com/residential_radiators/baseboard_uf.html) allowing a minimum 1" finished floor gap.
I have an older 1940s built home in which the radiators were originally down on the carpet too. I've since removed the carpet in favor of hardwood floors, but I think higher installation is good if for no other reason than cleaning ease, however I would put in a ceiling fan for forced convection before tackling raising all my radiators.