Are you still asking about a mod thermostat or a heat pump thermostat?
If it's a mod thermostat in a dual fuel system, then depending on the "aux off" set point you have programmed and the outdoor temp. If your aux off set point is 35 and your OD temp is 40, then no, the aux heat (fossil fuel) will not come on. If it were set to 40 and it was 35 OD, then yes, if the recovery feature were turned off, it would kick the system into high fire because you programmed it to do just that.
I can only assume that the standard blue thermostat in a heat pump application would have a similar setup but the question started about the mod stat