I vote absolutely no, but I would say that part of being a gentleman is being in a position to help others before himself, and, because we realize that people for the most part do judge individuals on their appearance and not their interior merits, a gentleman would realize that he may best be of service by dressing in a manner that socially puts others at ease.
So no, clothing and grooming are not requirements that define a gentleman, but I do think presenting yourself well in public allows you to exercise your usefulness to others in a wide range of circumstances.
WOW, +1. Perfectly stated.