In unarmed combat they would probably do well. A modern day MMA fighter would be physically inferior to someone that lived 2000 years ago due to genetic entropy but they would have superior training. I think it would be a Royce Gracie at UFC 1 type scenario. A 170lb pound guy choking out 220lb+ guys because no one knew anything about submission grappling.
Their people would kick MMA fighter's ass in armed combat with edged weapons but hand to hand, UFC fighter would beat most of them unless you got some pankration superstar and hes bigger than the MMA fighter. Pankration also allowed small joint manipulation and only groin attacks and eye gouges were illegal. There were no decisions. Fights went on until someone got knocked out or they submitted and sometimed theyd even kill. Remember there is no cut man, no doctor stoppage, no rounds. It was brutal stuff.
Arrichion, a pankration fighter died in a match but still got the win. His opponent had him in a choke hold. He used some type of technique to break his opponent's foot but the choke was still locked in. His opponent submitted but when he let go of the choke arrichion was dead.
Here is an interesting account of what happened:
Accordingly the antagonist of Arrichion, having already clinched him around the middle, thought to kill him; already he had wound his forearm about the other’s throat to shut off the breathing, while, pressing his legs on the groins and winding his feet one inside each knee of his adversary, he forestalled Arrichion’s resistance by choking him till the sleep of death thus induced began to creep over his senses. But in relaxing the tension of his legs he failed to forestall the scheme of Arrichion; for the latter kicked back with the sole of his right foot (as the result of which his right side was imperiled since now his knee was hanging unsupported), then with his groin he holds his adversary tight till he can no longer resist, and, throwing his weight down toward the left while he locks the latter’s foot tightly inside his own knee, by this violent outward thrust he wrenches the ankle from its socket.[6]