I would advise not building your entire character around it, but other than that it could lead to some interesting characters. Just focus on someone who happens to be a beggar, in addition to the bulk of their character. For example:
Janos Kralkov former veteran of the Crimson Legion, left destitute and lost with their destruction. After receiving no help from the lawful world that he had defended so righteously, he became an informant for the Silver Moon Syndicate crime lords, banding the city's beggars together to become their eyes and ears in the city of Regalia.
Or:
Buddy McSmileton is an Agni beggar that doesn't understand how begging works. He has a tendency to ask for things like socks or pieces of mail or whatever the person happens to be holding at the time. He has built a small igloo of begged socks in the Regalian undercity that somehow smells worse than the sewer around it.
What I would advise avoiding, however, is running around Regalia asking for actual money from people, and calling it roleplaying. Do something engaging, and expect to receive 'role play money' in place of actual money.
