I have two ceiling fans in my kid's rooms that have four lights on each
fan. These are controlled by a remote control which can dim them. I want
to use compact flourescent bulbs, but the dimmable flourescent bulbs are
ridculously priced, I'd spend over $120 for eight of them.

I'm thinking of wiring the coil of a relay to the output of the light
control module inside the fan, which will energize at probably any of
the dimmer voltages, and hook the four lamps all to 120V.

I'm wondering what the waveform out of the dimmer module looks like, and
if it'll work okay with an AC coil relay. Typically it's chopped AC.