It's hard to answer your question specifically because there are hundreds, if not thousands, of companies that actively recruit MBAs each with a different approach and philosophy. Generally speaking though, some industries (banking/PE/VC, consulting especially) do care very much about the name on the diploma and the top firms in those industries will likely only accept hires from specific schools. Beyond those industries, most companies have a target list of schools that they focus on recruiting from. That's not to say that they don't hire people from "non-target" schools, but those candidates are going to have to work a little harder to get themselves in front of a recruiter for consideration. Also, target schools tend to have a broader alumni network within the company, which current students can lean on for help throughout the process.
A good way to think about the MBA brand is that companies can use it to outsource initial applicant screening. If they're interviewing a candidate from a top 5/top 15/top 30 school, especially a school that they work with consistently, they already know that the candidate has met certain requirements from an academic and professional standpoint just to get in to the school.
In my experience (on the employer side in my before-school job and as a candidate), the accreditation of the school did not matter as much as the school's reputation itself, although for non-ranked schools an accreditation such as AACSB may provide some differentiation from non-AACSB schools.
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