No, there would be almost no purpose in bringing common criminals along with the army. Poor people, in general, didn't go to war. The middling classes of small farmers and townsmen generally provided the bulk of the infantry, while the aristocracy formed the cavalry and heavy infantry. Untrained, poorly armed low-lives of dubious loyalty would be nothing but an impediment.

One medieval (though they both carry on after as well) phenomenon may come closer to what you're asking about. Mercenary companies, usually infantrymen of the lighter sort, began to be used heavily in the 12th century in England and Normandy. Long wars and periods of unrest, first the Anarchy of Stephen and Matilda, then Henry II's wars and decades of suppression of rebellion, made reliable manpower necessary. Men had always fought for pay as individuals, but this was a bit shocking; large, organized independent companies of men under non-aristocratic leadership fighting purely for pay shocked contemporary (aristocratic and clerical) observers. The mercenaries were generally denounced as dubious individuals, existing outside the system of chivalry that bound aristocratic warriors together, if only loosely. They were purported to be especially talented at harassing an enemy's countryside; pillaging and burning villages, carrying off livestock, etc; but Welsh mercenaries were useful in Henry II's sieges, once swimming a river in their light gear to take a town from behind. The mercenaries were always an other, suspect if necessary, and almost always denounced as less than the knights in every way. Yet, it is telling that Richard I's most trusted lieutenant was a mercenary captain named Mercadier (whom the chroniclers reviled).