"The party has no choice but to incorporate the GMPC, just like it does any other PC"A GMPC is not an NPC. It's a Player Character run by the DM. It is the DM's personal mouthpiece and proxy, just like the characters are for the players. The party has no choice but to incorperate the GMPC, just like it does any other PC.
None of those apply to an NPC.
I think you run a very different game than I then, which may explain my confusion. In my games, no-one -- GM or player -- gets to run a character that the players would prefer not to have around. Our goal is to have fun, and not force people to accept an annoying PC.
If the definition of GMPC is "a character that the GM has forced on you and you have no choice but to incorporate" then I guess meh new answer is no, I have never run such a thing. Nor will I ever.