There are a series of answers that depend on why you want the degree.
If you are undertaking the course of study primarily to improve yourself and learn new skills, then the accreditation is a secondary concern - so long as it is not a diploma mill school (which this does not appear to be).
There are two benefits of a top tier MBA 1) More rigorous coursework which is driven by faculty and the peer group attracted the the school. For example, presenting a case study and having to defend your position when surrounded by a room of really bright people. 2) The network and door opening that comes with a degree from a "known-name" university.
In general, if I'm hiring and see a top-tier school, the implication is that the individual is above average smart, motivated and able to compete. They still need to pass an interview and be skilled, but much of the culling has been done. That being said, the top-tier schools feed the top-tier firms or people that are looking to climb the biggest corporate ladders. Again, this gets back to motivation - why you are doing this.
If I see an MBA, particularly a mid-career MBA, but not from a school I readily recognize, once I satisfy myself that it's not a diploma mill school, then I think very highly of the candidate in terms of trying to improve themselves and learn new skills. So in the long-run it potentially nets out.
With respect to your original question on accreditation, top schools are AACSB because it is a national accreditation. However, good regional accreditation are fine. This article is a good
summary.
Since your employer is sponsoring this program, aside from your own personal time commitment, there's not much to lose, and certainly much to potentially gain.