I suspect Homeseer does support Aprilaire. myServer does. And myServer integrates with Homeseer...
I haven't checked if that model is supported by our current AprilAire driver. I suspect it would be.
One thought though, is buy a lesser expensive thermostat and "hide it" (certainly accessible to the room temp)...and then put a touchscreen on the wall that controls the entire home system (Homeseer or myServer or both). Certainly check that the thermostat is compatible with your control system (Venstar is best as it's local WiFi...Honeywell, EcoBee, Nest are Internet based and not recommended - but would work).
That way you get way more functionality out of the wall acne than just a nice looking thermostat.