I was waiting to see if anyone else replied, but since it's been quiet, here is what I'm thinking. My initial concern was the in-rush current if the thermostat tried to switch everything back on, because the AC would be set to the compressor+fan mode and it would try to start up everything at once. This site
http://www.2manytoyz.com/yamaha2400.html has a guy who bought a Yamaha EF2400iS generator and then tried out several things in his travel trailer to see what it would run, and the little 5 kbtu window unit that he started with showed 22.6 A startup current when he intentionally abused it by running it for a while, cutting it off and then immediately cutting it back on. It is extreme, and I'd expect that if the compressor had been off a while he'd see a little less than half that, but it's still a problem for a typical attic fan thermostat. I think that much current switching on will wear out the internal switch contacts pretty quickly.
However, it's possible that the typical usage cycle here in Colorado would be: turn on the AC in the afternoon after everything is baking hot in the sun, and the AC runs like mad until after the sun sets. Some time later, maybe 9 or 10 o'clock, the interior finally cools enough that the compressor doesn't have to keep running. Some time shortly thereafter, maybe before midnight after the outside temperature has lost 20 or 30 degrees, the fan can cut off and the unit stays idle until morning. In the morning you get up, turn off the AC, and turn on the Fantastic Fan for morning activities. So the in-rush would never happen (because of manual intervention in the morning). And then again, maybe it doesn't matter and it would all work just fine.
Anyway, if you try it and get it to work, let us know!