After a random encounter with the morton brothers, the one who comes back for revenge, Vic has stopped responding to any input. Every time I click on him, he will say something like "I've had it!" and just stays where he is. Even though he will not move, he still follows me into transitions to different areas.
I haven't hurt vic in any way during that fight since I was going unarmed (although earlier on, long before that random encounter, I accidentally clicked on him and knocked him down AND crippled his leg XD. Immediately afterwards, he was fine though... ). Examining Vic always says that he is unhurt, and does not mention anything about broken limbs.
So he is now still a part of the party, but cannot be interacted with at all since he just says "I've had it!" Reloading doesn't help, because I kind of saved immediately after the fight. I've already leveled him up, do I have to kill him to cut him loose?

Try telling him to wait and then let him join again.

I can't. Like I said, he won't respond to anything, since he just states "I've had it up to here!" every time I click on him.

Use him as a meat shield, at least he will be usefull for something.
Now serious, Fallout 2 v1.0 SUCKS!
Make yourself a favor and download Killap's Patch/Restoration mod, you won't regret it.
Just a friendly advice.

If Vic spawns next to you after loading new areas (after becoming apathetic), will he count towards the companion cap unless killed?

Well, so it is Feature, not a bug? I had this problem, too, and I just hit him and he snapped out of it...