I installed a Pergo floor about 2 years ago in a room with radiators. Have had no problems at all with warping from the radiator's heat.
You do need a relatively level surface to lay a floating floor on. (I got away with flooring over a wide doorway that had a slight ridge to it, and it hasn't given me any problems. Note that it was a slight ridge, maybe 1/2 inch gradual drop, certainly not a 1"-2" cliff.)
It shouldn't be very difficult to fill in the hole under the radiator. It won't get walked on, so I wouldn't be too concerned about securing it down - - maybe just some construction glue. Just get a sheet of plywood (of the right thickness) cut to the right size and slip it in under there. The only thing that might look weird is that your radiator will seem to have very short feet, and the radiator body will sit very close to the floor.
Cutting out for the feet isn't *too* bad depending on the layout; there are probably instructions for doing that with the flooring. You can cut a big enough hole directly through the laminate with a circular drill bit (I call them keyhole bits; not sure if that's real name), then cut the board straight through the hole parallel to the radiator, so you end up with a short piece with half of the circle. That goes against the wall, with the open half-circle cradling the foot, and the board with the other half of the circle goes in front of the radiator. If you fill the parallel cut with patching material that matches the flooring (made by floor manufacturer), you'll never see the cut.
You can get silver flanges to slip over the radiator pipes (might look weird on the feet though), so you can hide some sins that way.