You'd get executed regardless, and I know of no counterexample. Generally, this was a form of capital punishment, known as damnatio ad ferrum or damnatio ad gladium. This variant would give you no hope to escape your sentence. Essentially, you were convicted to die in the arena by fighting against others with the same sentence, fighting in pairs. The survivor would go against the next convicted until the last man standing. But he would have little joy in his victory, because he would then be executed. Possibly, a gladiator dressed as Dis, god of the underworld, would club him down with a hammer. The only possibility for mitigation was to go on living a bit longer by fighting well. Should you and your partner decide not to fight each other, they would find ways to motivate you.

Seneca recounts, with obvious distaste, such a spectacle in a letter to Lucilius:

By chance I came to the Arena on midday, expecting games, fun and other relaxation, where human eyes can relax themselves from the view of human blood. But far from it: Whatever had been fought before was mercy in comparison to what came, they omit all jokes, now it's only murder. They have nothing with which to protect themselves, since their whole body is exposed to blows they never strike fruitless. Such things most people prefer to the ordinary pairs [of gladiators]. And why not? No helmet, no shield defends the blade (ferrum). Protection, for what? Technique, for what? All that only delays death. In the morning, they throw humans before lions and bears [referring to the equally deadly damnatio ad bestias], in the midday before the audience. Murderers they have fight Murderers and determine the victor for another carnage. For the fighters, death is the way out.

Seneca probbly expected some sort of lighter spectacle, that was often held after the morning events of gladiatorial games, with play-fighting Gladiators and other light entertainment. For him, the brutal death of the convicts lacked the artistry and moral qualities of a real gladiatorial fight.

A variant of this was to put you to fight against a real gladiator, but without any protection against a trained fighter chances were very slim. And even if you managed somehow to overpower him, you are sentenced to death. This was just a variant of the executions that were held during gladiatorial games, other variants being burned alive or thrown to the beasts. It probably would play out the same as if you'd win a fight against another convict. Ending in death.

The milder form would be the damnatio ad ludum gladiatorum: This would condemn you to life as a gladiator, which sounds worse than it had the possibility to be. The life of a Gladiator was dangerous, but not every fight ended in death. Gladiators were the star athletes and sex symbols of Ancient Rome, and their popularity among the lower classes knew no bounds. This was a very popular form of punishment and an important source of recruitment for the gladiatorial schools, but it was no capital punishment.

In conclusion, I highly doubt that they would have let him live if he was convicted to one of the first two types of punishment. They were capital sentences, and death was the desired result and outcome for the state. The odds were stacked against the convicts in any case, having to fight each other or the gladiators with no defensive weapons and only a sword for themselves, against a trained fighter.

I don't have the episode before me, but I might give it a watch once I get home if I have the time.

Based on your description, the answer is probably no, this would not have happened.

I've never seen the episode or the show, but I assume there are some historical anachronisms that make it good television. To put it simply, gladiatorial combat was very distinct from an execution. To be sure, many gladiators were put in situations with long odds (think of fighting a lion with a fishing net and a knife!), but there was nothing to stop gladiators from emerging victorious in the face of those odds. Executions were separate from gladiatorial bouts, though both enjoyed primetime slots in amphitheaters throughout the Roman Empire.

The only time a gladiator would be "condemned to die" would be in a situation where he had already lost the fight, and would be physically incapable of reengaging his opponent in combat in any meaningful way. Once this had been achieved, the victorious gladiator would look for judgment on whether to kill or spare his defeated opponent, usually from the highest-ranking official present - though this decision was ultimately left to the crowd quite frequently.

So the answer to your question is no, that would not have happened in real life. Those condemned to die in a gladiatorial bout would have already been incapable of resisting any further. And if the characters in question had been there simply for execution rather than combat, then barring any Hollywood-esque heroic escapes, they would have been killed regardless.

This is my first post, so do let me know if this answers your question.