Yes it's possible but...
Firewall is completely different. Heater core lines exit in a totally different spot, same for the blower motor. A/C cars didn't have a vent box on the driver's side, so, if you want a vent there you have to add that too. Heater control panel and the bezel that surrounds it is different, so you have to change that too. And then of course the dash doesn't have the A/C vents in it. Oh, the defrost duct is different. The defroster outlet is a different shape and slightly moved on the heat only box, so you have to change the duct over too. Which is a real pain because the screws that hold the duct in at the top are covered by the dash pad.
I just did all this on mine. I patched the holes in the firewall for all the A/C stuff and added the holes for the non-ac heater box. I also had to find a heater box and restore it, fun stuff. I was just tired of all the vacuum operated doors in the A/C box. My car hasn't had the A/C hooked up for quite some time, it didn't work when I got the car (maybe the A/C, maybe all the vacuum operated crap, probably both). After I removed all the A/C stuff out in the engine bay I tried to sort out the A/C heater box, but I could never get all the vacuum actuators working right. So, even the heater didn't work the way it should have because I had limited control on the doors. The non-A/C box with it's cable controlled doors is way easier to deal with. And pulling all the A/C stuff must have saved some serious weight. Even the heater box is quite a bit lighter.