I remember reading in a Mustang Monthly I think that only the pre-'87 non-ac cars can be easily accessed through the glove box. Before I took my '90 apart, I couldn't find any way to access the heater core only through the glove box, A/C lines or not, they are not the only things that make the heater case difficult to get to. The panel on the heater case that reveals the core opens on the top and its a bitch to reach the bolts back there, among all the other crap thats stuffed behind the dash.
But like you said, do some more research and find out for sure, from my experience I don't think you can reach the core just through the glove box even on a non-a/c 87-93 car.