I am sure a medievalist can comment but the trope of a "brave adventurer" did at least exist to some degree in the middle ages, which is not the same thing as saying there actually were people who would satisfy that definition at the time.

One of the popular myths of the medieval period is that of Alexander the Great. "But wait, he's not mythical" — yes, I know, but they had amazing myths about his supposed adventures. The Alexander stories are kind of amazing — Alexander invents a submarine, Alexander goes to outer space, Alexander makes robots, Alexander "fought serpents with emeralds in their foreheads," Alexander defeats king after king, Alexander "found a spring where cooked fish came back to life," and on and on and on through his "adventures" in Greece, India, and beyond.

I don't really have a full sense of what one should make of this Alexander mythos that spans centuries of writing — Did people think it was real? What role does this kind of "hero" play in medieval writings? What is fully going on in these stories that, at times, seem like a mixture of fantasy and even science fiction? If I were a medievalist I would totally veg out on the Alexander mythos (it is so odd, yet so obscure!), but I am not, so I can only offer it up as a possible thing for others to riff off of.

I've talked a little bit about specific aspects of the Alexander stories, linked above, and reference E. Truitt's Medieval Robots, which talks a little bit about some aspects of the Alexander stories (specifically the ones with automatons, which are a medieval trope). Wish I had more to offer, though.

If you're asking whether a barbarian, an archer, and a dwarf would walk from town to town doing fetch quests in medieval Europe... no. It would be an interesting question to ask whether the Crusades, as reality or popular trope, would satisfy that definition, but I am not an expert on those at all.

In the sense of "half a dozen people wandering from city to city fighting enemies and solving problems," not as such. However, there were people filling broadly similar roles.

There were a lot of outlaws in the Middle Ages, particularly in England, thanks to changes made by the Normans to the country's legal system. To massively oversimplify, it became easier for individual villages and towns to dispense justice, which often meant declaring a person an outlaw. By the later Middle Ages, this system was sufficiently abused (combined with other factors) that outlaws were often viewed sympathetically (partly explaining the popularity of Robin Hood). So, people living off the land, outside of the system, existed.

In addition, a significant percentage of soldiers going off on the Crusades were essentially mercenaries--outlaws and other persons of, er, questionable origin--who were hired precisely because they had learned to live by their wit and weapons. And if they survived to return to their home country, many would travel around bragging of their adventures and/or return to brigandry.

So, there certainly were groups of combat-hardened people living vagabond lives outside of normal civilization. But they weren't "brave adventurers" in the RPG sense.

Source: Terry Jones' Medieval Lives, an admittedly pop history view of the period but very easy to read and understand.