Actually I think the Floris Mod pack lets you do this.
I got a scene with one of my veteran troops where he pledged to follow me to the ends of the earth, and then he became a companion character. His name was stuck as the troop title though. It only happened once, and I've never figured out exactly what caused it to occur. I can still remember the guy's quote. "For you my lord, the blood on my sword shall never dry!"
If someone knows what specific mod in that pack made that possible I would dearly love to know, cause that was awesome.
That aside. It is a very cool idea and it may work here if the companions work the way I think they do and they are largely generated. No Bunduks, Artimenners or Jerimus's here I'm afraid.
As for the idea breaking the game... I doubt it. As long as it is at least kinda rare I don't think it'll be an issue. Equipping and training just a few companions was expensive, dull and time consuming in Warband, and they never really accomplished much more than the regular soldiers. While the potential for abuse is there, I guarantee there are going to be far easier ways to break Bannerlord than companion spam.