Visiting professor's office before being admitted to PhD program?
It sounds like an excellent idea.  I like to meet with prospective students, especially ones from atypical backgrounds; a meeting gives both applicant and faculty a chance to gauge whether someone will be a good fit for the program.

However, don't get too pushy.  Keep the conversation casual, and don't put on an elaborate show of your knowledge.  The best approach may be to ask about the professor's research, and express how it tied into what you already learned and found interesting, as well as what you are interested in studying further in the future.