Based on your goal (to have a small rental portfolio), I am not sure the MBA would be ideal.
I am an advocate of education, and if you told me you wanted to work in Fortune 500 Company and were looking to kill it in an MAB program, make connections, and start your rise, I may so go for it.
Even then, I am not a huge fan of the debt, however (sort of going Dave Ramsey there).... So if you could cash flow it, even better.
Also, you may know a traditional business path is to work for a large company a few years and if you are promising then they pay for the executive MBA (though it may be the nearby state school or even be online, maybe not top 20 but usually AACSB accredited). Then the company retains you (win/win) and gets a future mid/upper level manager.
My understanding is that you then often expect or put for a promotion soon after the MBA (some folks may seek other opportunities if there is not upward mobility or don't get he move up).
At any rate, you may be able to find a lateral move to a business (maybe one with science-related operations) work there and utilize their MBA program for new/promising executives.
Or, along the same lines, you could keep your current job and put together your own career plan taking the MBA on the side. Some top 50 ones are low residency now. Some of the executive/online/low residency MBAs may work with a day job.
Finally, perhaps the bad news....Not that much of the major US graduate business curriculum will cover real estate transactions and management. I think Cornell may have some major hotel/hospitality type property management--but buying a 4 plex not so much.
Oddly, the real estate classes at a community college where a 30 year broker, appraiser or long time property manager teach may be more akin to what you seek. Not much prestige--but more applicable.
Finally, you may want to get a school of hard knocks MBA by doing deals, reading books, listening to the podcasts, meet ups with local investors, trying some hands on work (tape and mud to screening tenants!). That costs is about free at the library and no extra charge to be DIY landlord on your next rental!