If the ending of the game wraps up with your Jedi going in to hiding, then it can work. Obi-Wan was a Jedi, yet he was able to go in to hiding without much problem. Why is it a stretch to think the new PC can't do the same? Solve whatever crisis takes place in the game, then at the end he disappears into obscurity like Obi-Wan did. It's a big universe. It's not like the entire galaxy would know who he is everywhere he goes.
They don't have to know the PC is Force sensitive. Look at Taris. The planet was under Sith quarantine and looking out for an escaped Jedi, and two republic fugetives, yet you, Carth and Bastila were still able to walk freely and interact with the general population. Sure some might call that a plothole, but the point being if done properly, the PC just has to be "under cover" to hide his true identity.