1986 Subaru GL wagon 4x4

Is it necessary to drain the coolant when replacing the timing belts? I ask because I recently had this done and discovered a few days later that the engine was overheating. When I drained the antifreeze I got only about 1 quart of old looking fluid out of it. I filled the radiator with water, but it now uses water without a visible leak at the rate of about 1 quart every 20 miles!

I now assume that I have a head gasket leak, what do you think? I think the repair shop forgot to refill the radiator unless they did not need to drain it to replace the belts???

Thanks