Yes, though not to the level of king.

In fact, one particular group supplied a large amount of these unlikely candidates for social advancement: mercenaries. Mercenaries had a very interesting role in the Medieval world. They came from a plethora of backgrounds: men-at-arms, bandits, knights, and even some were members of the nobility. However, they existed on the fringes as social outcasts. Men who killed for a living were detested by the Church and official authorities who had to fight them. Conversely, they were widely respected for their military skill and prowess by their employers. These skills went beyond the battlefield but also into managing logistics, carrying out sieges, and garrisoning and protecting strategic areas. They also were a much needed source for reliable manpower as feudal servants often proved recalcitrant to offer service at their own expense. Thus, mercenaries were men who were socially reviled but also respected for their military abilities who were always ready to serve so long as one had the money to pay. This put mercenaries in contact with the people who could elevate them into a life beyond paid military service.

There were a few good reasons to integrate a mercenary into the nobility. Firstly, it allowed one to secure their services and their troops to their side. Mercenaries were really good at military affairs, often times far better than the levied troops whom they faced off against. This meant that if one did not have them on their side, they could easily be weaponized against their former employer. So not only did they earn them as a vassal it also gave the former mercenary a stake in the realm he had been integrated to. Secondly, it allowed one to peacefully demobilize them, preventing them from turning into brigands. Medieval Languedoc had an abundant presence of mercenaries due to state of constant low level warfare in the 12th century. In between contracts they turned to banditry to make ends meet. The bishop of Toulouse complained how these mercenaries would waylay him on the road, preventing him from visiting the churches in his diocese. Local lords took to charging people protection tolls to guard travelers due to how unsafe these mercenaries made life outside the castra. The image presented is that daily life was seriously disrupted because of the banditry of unemployed mercenaries. Therefore, a lord had good reason to look past the low social status of mercenaries when the well being of their domain was at stake.

One lord who elevated a mercenary was Phillip Augustus of France (1180-1223). Phillip extensively used mercenaries throughout his reign due to constant warfare with his neighbors. In particular, he retained the services of Welsh mercenary Lambert Cadoc who had defected from the English under Richard the Lionheart to Phillip's side. Cadoc earned a reputation as a very capable warrior who would prove instrumental to Phillip's campaigns against the English in the Anglo-French wars of the early 1200s. As a reward for his services Phillip awarded Cadoc with a number of fiefs and titles, accruing further boons over the course of his life in service to the French king. In doing so, Phillip aimed to permanently retain Cadoc's service and integrate him into the royal administration. Cadoc's social reputation was sufficient enough that his daughter would even marry into the minor Norman nobility. Thus, Cadoc appeared in the annals of history as a mercenary bowman and ended life as an important French lord and royal administrator.

Sources*

• Military aspects of the Albigensian Crusade by Rachel Louise Noah - particularly her treatment on mercenaries in 12th and 13th century France. Cadoc's case was discussed here.

• Institutional History of the Albigensian Crusade by Claire Dutton - particularly her treatment on mercenaries in the Languedoc and France at the time of the Crusade

• Warfare and the Composition of Armies in France, 1100-1218: An Emphasis on the Common Soldier by Laurence Marvin

• "Mercenaries and Capuchins in Southern France in the Late Twelfth Century" by John France in Shipping, Trade and Crusade in the Medieval Mediterranean

*I mainly study the Albigensian Crusade which extensively involved mercenaries. Much of my bibliography on this question draws from that conflict but many of these treatments do analyze mercenaries in a broader context.