Motion - like you, my amateur radio training tells me that the class C amp is not appropriate for anything other than CW or FM. It might work or might not work depending on how tolerant the receiving system is of a distorted signal. In the process of distorting the signal a bunch of interference can or will be generated which can cause a whole bunch of other problems. I'd worry that you might put one together and find that it does work based on the RC systems response to commands but unknowingly anger some others with the unintended interference.
With the right adjustments you might get the amplifier to operate in a more linear mode however with significantly less power.