I see. You definitely would need to consider how that fits into the desired campaign narratives. If the whole campaign is about freedom fighters opposing Lord Ajax, it makes little difference if one character starts out as more of an outlaw than another. But if the campaign is meant to be knights of the round table doing quests for the one true king, it might be more of a problem if a player has to have a secret identity or sit out most social encounters. I wouldn’t want to impose that situation on a player unless they are specifically interested in playing that role.