Don't get me wrong either I don't like the idea of doing this as a back up either and believe if you really felt you needed the security of a back up an on off type Thermostat is the best way to go!
But as for the math and science it should work. Also you have to remember the resistances are not changing and the proportional T-stat has a max voltage output. Even though the Proportiona T-stat is capable of supplying 400 Watts of power it can only supply 120 VAC or some other voltage lower depending on manufacturer. The resistance of the heat mat is based on a given voltage (Normally 120 VAC, 110 VAC, and 220 VAC if in europe.) So say it is rated for 20 Watts Amps = Watts/Voltage
Amps = 20 Watts / 120 Volts = 0.166666666 Amps.
Resistance = Volts / Amps or 120 Volts / 0.166666666 = 720 Ohms. The value of resistance is not going to change regardless of the actual applied voltage. So the Proportion T-stat will not be able to push its full rated watts out through this singel load. You have to have multiple heat strips in parallel to get close to the max watt rating of the controller.