In MechWarrior tabletop RPG character creation (using life paths similar to HBS) a mechwarrior was required to serve at least one 2-year tour of duty in a house unit upon graduating from an academy. After that you were free to choose your future career. Leaving a safe job in a well-supplied house unit for the uncertain life of a merc is probably something not many would consider, though. It's not illegal unless you turn straight to shady stuff like piracy and assassinations. But your reputation would certainly take a hit, your family would probably disown you, and your former house military wouldn't trust you.
Morgan and Patrick Kell actually got started this way, graduating with top marks from Nagelring, then serving with the Skye Rangers (a fairly odd assignment considering their Steiner loyalties) and eventually founding the Kell Hounds. However, the Kells were a) extremely skilled, b) independently wealthy, being minor Lyran nobles and c) were already favorites of the Archon.