Possible - yes.
Likely - no.
I agree with Grumpydonut, it's not a disorder that goes away after a while, they can work in therapy on the triggers and how they respond to them, but in the end it's an unstable long-pattern.
Will their friends a family eventually realize that the person with BPD is unstable?
I think that my pwBPD's mother is the only person who really realized how unstable he is. Even his close friends and his childhood friends, who he hangs out all the time only have a vague idea. They think he's "a lil crazy", very impulsive and sometimes throws hands. But they approach it lightly, they laugh and joke about it. They have no idea of the pain he causes and how devastating his splitting is.
My pwBPD cares a lot about his façade, we never had a fight in front of other people, he never mistreated me in front of his friends/family. Even if we had a catastrophic fight 5 minutes earlier, he'll then act like we're a perfect loving couple so he can keep his image.