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Can strong work experience counter a lacking traditional research background?
No. Those years will be largely wasted, and can even hurt you in the admissions process.
And finally, I've always been aware of a stereotype of academic inbreeding in higher-level academia. Would having my MAC at UNC prevent me being strongly considered as a PhD student there?
It will not. If you make an impression on professors it may very well improve your chances.
I'm already a huge Tarheel fan...
This is a really bad reason to go to UNC, although yes, it is quite a good school. UNC typically takes a large cohort of accounting PhD students, but your odds of getting admitted there are still very, very small. A higher percentage of applicants gets into Harvard Business than will get into most accounting PhD programs.
I'm sure I'll be taking a lot more as the year goes on, but we won't dabble in calculus too often.
You should really take calculus and linear algebra now. Take them as electives!
I realize this is VERY early on, but I generally plan pretty far in advanced... Having an end goal keeps me very motivated!
My advice to you is to see if you can get some RA work. Tell the professors you are interested in research and you want to help them with their's. Learn what it is you are getting into, because I don't think that knowledge is reflected in what you've written so far. If you want to do a PhD, those MAC classes don't mean much. You need economics (NOT business economics), statistics (NOT business statistics), and math (NOT math for business majors). It's not expected you will have all of these when you enter the program, but this is what Adcoms look for.
If you are entering your last year in the program, you should be able to take the calculus sequence. Do so. Become an RA, compensated or un-compensated. Start planning how you can get the three best letters you can. After you graduate, get a job. Your hours will be restrictive, so you may not be able to take on additional coursework. If you can, take Linear Algebra. In either case, begin studying for the GMAT. Search my post history for GMAT specific advice.
If you have calculus, research experience, strong letters, a good GMAT (90th percentile quant/90th percentile verbal is the unofficial cutoff for UNC, or so I was told) and good GPAs, you will be competitive for UNC and similar schools.