It depends? If there's an immediate concrete benefit and they're planning to stay regional anyway? Possibly/probably? And a lot of people actually stay with an employer for a significant length of time. And even just using as a near-term/midterm stepping stone may pay benefits down the road beyond the degree itself.
I tend to think personally that law and MBA grad degrees do generally tilt toward benefiting top schools but I'd never suggest that was an ironclad rule.
The next question is, how long does the affect of the college you attend vs. experience matter with an MBA?
For software development, from personal experience of going to an unknown state school in the mid 90s, I was just as competitive with people coming from well known schools within three or four years. It probably would have helped with me landing that first job.
Again, I think it depends. My MBA definitely played into my first job after; the process started with an on-campus interview. I doubt the school (or probably even that I had an MBA) made a bit of difference after that but then I was in that job for 13 years and my subsequent jobs weren't even business roles per se. I think the background was useful but it didn't matter from a hiring perspective if I had a degree from X school or not.
In my current job, to the degree my educational pedigree made any difference at all, it was my undergrad because that's where my hiring manager went. However, I'm sure there are many cases where business school networks associated with top schools can be important.