Truths to Work Into A Solution:
- No one likes to be killed/defeated by fiat if they think they could
- It's possible he's doing this to get attention
- The other
players should get something to do too
Result: I would play it out, but alternate spotlight time with the rest of the group, giving them more.
The other players are doing something while this PC is in their own world, right? Cut back to them and have them do whatever (with a sharp eye against the metagaming of "Uh, I suddenly decide to go for a run to find Julio"). Give them plenty of time. Then cut back to the combat for a couple rounds, and back.
This has the result of being fair to the solo combatant (and really, shouldn't D&D let people have solo combats from time to time?) and lets the others have equal spotlight time. Giving them a bit more helps dissuade him from doing this if he just wants attention.
Although, does he fade into the back in group situations? It may be a fair allocation of spotlight time already. I know sometimes I get frustrated when I am playing a PC who wants to do solo combats, honorably challenge a specific foe, or whatnot and my party is always kill-stealing.
I had a situation like this in my Reavers campaign recently. The monk went in and fought a whole installation of pirates without the rest of the party. On the one hand, he got beaten and captured, but on the other hand, he killed half the pirates so that when the rest of the PCs came they could mop up more easily (though he did then get used as a hostage...). The story outcome was entertaining enough, and I studiously swapped time back and forth between him and the others, so all was well in our eyes.
Also, there's only so long it could take, right, if it's a sure-lose situation? If it goes on very long, then by definition they have a chance to pull it out, escape, etc.
Oh, one other suggestion I've used from time to time - give the PCs some of the bad guys to play. This reduces your work, gives them something to do, and makes the opposition a lot more effective.