No, that's movie stuff. Many Republican soldiers probably had less weapons training than a gladiator, who trained with his weapons every day. Former gladiators were often used as ruffians in the Late Republic, and at times they could even be recruited as good soldier-material (App. B Civ. 3.49). It's possible that Roman soldiers, who we know did a fair bit of weapons training under a strict general (Pol 10.20: note they only did weapons training every few days), around the time of the Late Republic adopted gladiatorial training techniques for training soldiers (Southern 2006 94-5). This is in the context of Gaius Marius taking command of an army whose previous general, Rutilius Rufus, had already adopted these training techniques. Marius apparently was so impressed he kept the training regime intact and expanded it to his newly raised legions. However, in general Roman armies had no modern 'doctrinal' system of training (though they all learned similar skills) and would have had different training regimes under different generals.

A gladiator and a legionary were trained for different tasks. A gladiator is a showy, athletic fighter of single combats, and he trains entirely for this task. A soldier has many other tasks beyond fighting, and he spends much time doing other duties beyond training to fight. An individual soldier in general was probably no match for a gladiator unless he was fairly experienced. En-masse, of course gladiators would have been little use on the battlefield compared to professionals trained in manoeuvre, tactics and fortification. The Third Servile War saw some exceptional success on the part of Spartacus, in that he met some success against legions of raw recruits that he heavily outnumbered, but gladiators quite simply did not have the broad skill-set that Roman soldiers used to conduct successful wars. On the other hand, the fact that the state took greater control of gladiatorial training after the Spartacus uprising might have meant that gladiators got even better quality training! They were certainly popular as bodyguards and hired muscle in the Late Republic.

In general individuals did not perform well against multiple opponents. Individual fighters beating multiple trained and/or experienced opponents is something that happens a lot in movies and TV, and has almost never and continues to almost never occur in the real world. Examples of such things can be found (Josephus BJ 3.232, 6.61-88: these citations are a bit off because the Penguin edition is terrible), but they are fairly exceptional and unusual occurrences, hence why they pop up in the literature.

Regarding the scene in Rome, I have to say to be fair, Pullo blindsides them and incapacitates two straight away (extremely unlikely of course), while as is usual in movies and TV shows where one character fights multiple enemies, any enemy who is off-screen for any amount of time stands around and does nothing. But Pullo then fights one-on-one and we see something resembling a fight, until more enemies charge on-screen and the Inverse Ninja Law kicks in to make Pullo an unstoppable killing machine. As I've said above, there are a very small number of mentions of one or two men beating off and routing larger numbers of men in ancient warfare, but these instances are so exceptional that major writers go out of their way to mention them, yet I can count on one hand the amount of such accounts I have read. The enormous prestige associated with stripping a single enemy of his armour shows that just killing one enemy was hard enough for everybody to respect you for achieving it.