Hi,
I can't tell you for sure about the HAI models but the RCS 3/2 stage thermostats can be used with 1 stage heating/cooling.
With the RCS it works like this: you configure the thermostat with 3 heat "delta" settings and 2 cool "delta" settings. The delta settings control when the various stage relays turn on. For instance let's say the 3 heat deltas are set to 1, 3, and 5. When the room temp drops below the heat set point by 1 degree the 1st stage heat relay will close. When the room temp drops below the heat set point by 3 degrees the 2nd stage heat relay will close (the 1st stage stays closed). When the room temp drops below the heat set point by 5 degrees the 3rd stage heat relay will close (the 1st and 2nd stage relays stay closed).
The cooling works much the same.
So if I only connect the 1st stage heat and cool relays to my 1 stage heat/cooling system it will work just fine, the other relays will activate but since they are not connect nothing bad will happen.