I would say yes, but that personality is what YOU give it by decorating and furnishing the room. It isn't necessarily inherent to the space. Windows and the scene outside them, however, could alter what decor and furnishings would make the room feel a certain way as it would, in a way, be part of the overall feel of the space.

I'm sorry if this is a bit vague; without seeing the space in question, I can't really think of anything more specific that might help inspire an idea.