Does where you get your degree at make that much of a difference?

I'm a non-core MBA student (however top 20) in a part time program, looking to score an internship with an IB. I'm a GWOT Marine Corps veteran and I've got 4 years of experience in M&A Advisory as a consultant. (Think DD)

I recently had a SD with Goldman Sachs. Great interview. Really enjoyed it. Thought I did well, but knew going in that I was already fortunate to even have been selected. I was the only 1 of 45 people selected for the SD that was non-core. Everyone in my time slot was Wharton.

After I received my answer that I didn't get the offer, but that I was still being considered for a position outside of the NYC office, I chalked it up as a great experience, potential opportunity elsewhere within GS and that school probably played a role in this selection round.

How often does school selection come into play during post-SD selection?

Disclaimer:
It's much harder to get into a target school than the one I'm attending. I completely appreciate that if I were at a bank, I would go to the absolute best schools to recruit. I wouldn't blame a selection team for wanting to recruit from top schools. I'm asking in order to inform my strategy moving forward.