Applying to PhD Programs after time in industry

I've searched around and looked at this question which is quite similar but I have some further questions.

I'm an undergraduate currently (Math and Computer Science majors) and I've been spending most my time and effort taking courses and research for the ultimate purpose of applying for a PhD program in (Pure) Math.

However, I'm starting to question my desire and aptitude for grad school (and subsequently academia). I am considering getting a programming job upon graduation and seeing if I really miss doing math research enough.

Does the fact that I'm even considering this mean that I probably shouldn't go to grad school?

I imagine that after working in an unrelated programming job for a couple years that I wouldn't look very dedicated to admissions committees. In the question I linked to above, one of the answers mentions a way around this:

"I happened to live in the same city as an excellent university, and I asked a professor if I could sit in on his grad class. He kindly agreed, and I worked very hard, solved all the homework problems correctly and wrote them up, and slaved over my term project."

How common would this kind of scenario be? I happen to attend a very research happy university so it is very easy for me to find opportunities as an undergrad. If I enroll in some local university as a non-degree student, will I still have access to faculty and so on to try to do research?

Is it ever acceptable to read up on the work of a faculty member or post-doc and ask to discuss their problems, etc... if I wasn't affiliated with the university at all? I would imagine that they wouldn't gain any credit for that as far as their advising duties, and thus they would likely not be interested (being as busy as academics tend to be!)