Possible,
but chances are very slim.
Persistence together with sincerity can only work, unless she is
willing to give you a chance. If not, it's like trying to knock
down the wall with your head. In this case where the girl initially
reject - throughout the cases I encounter/hear/shared/adviced/etc,
maybe my memories failed me - I don't recall one entering into a
relationship and last happily. (My constant variable has to be that
this girl is SINGLE, then and now. If she was attached when the guy
chased her, its a different scenario) 
Cheers
