No, that's never happened, even on the coldest days. It's working hard when it on 10 minutes, and off 20 minutes, or 33% duty cycle.

I don't think any HVAC contractor wants to risk that a furnace will fall 10% 'short' on the coldest days, so they upsize the rating.

That, or running the blower fan 24/7 would burn it out.

I would think that a 50,000 BTU unit, with a 2-speed fan, low for heating, high for cooling, would be a bit more efficient, since you would not have the losses of the heat up/cool down portion.