It works well. In fact, that's exactly how professional racks (ARS, Freedom Breeder, etc) are designed. Each level has an individual heating element, which all plug into a power strip/surge protector. That strip then plugs into a single thetmostat.

It's not a matter of "it could be done". It can be done successfully and has been for quite some time on a large scale. You just need to ensure that the heating elements are identical (wattage, size, length, etc) that you're plugging into the strip and that the thermostat can handle the wattage. Beyond that, it's just a matter of how many animals you personally feel comfortable with having on a single thermostat should something go wrong.