I check the manual and it says to pull the box. It might be possible but part of the problem I see would be trying to get to the clips that hold the top and bottom halves together off on the firewall side.
I guess if you loosen the firewall and cowl mounting screws you might be able to access them. Might also need to loosen the blower motor The heater core is in the bottom half.
I would bite the bullet and go ahead and pull the whole box. I know having ac makes it a pain due to having to disconnect the lines and then recharging the system but by pulling it would give you the opportunity to replace any of the gaskets and seals if needed.
Unfortunately I'm sure the box has to come out. The clips have to be taken off a certain way to prevent chipping or cracking of the housing. I made this mistake, and found that finding a good used original box is very difficult and expensive. Usually the boxes have been broken by previous owners trying to service them, or the drain hole nipple is broken or the mounting tabs are broken or cracked. This is something you want to be careful with. If you don't care about originality the aftermarket boxes are actually decent enough. But like Kilgon said, the back clips will be very hard to access. Good luck!!
Thanks for the input fellas. this wasn't for my car. This was a question asked by the gentleman that I restored his 71 mach1. He text me the other day asking about it because his is leaking. He asked if I was interested in replacing it, but with the 65 taking up most of my garage I cant get him in till that's done. I remember them being a pain in the ass to get out without breaking something.