Factor of undergrad Prestige in becoming a Quant

I understand that becoming a quant requires at least a masters and Ph.D and that risk analysis and similar desk analyst roles are completely different jobs than investment banking, but is there a similar "target school/semi-target/non-target" attitude in which getting a quant job is largely dependent on the amount of recruiting or interview spots for one's undergraduate college, or is it similar to a programming/computer science job in which roughly everyone is paid on a similar scale (except for a handful of elite) with a lot of upward mobility for salary, and undergraduate institution doesn't play as big of a role as it would for IB, and instead grad school is what matters most? Also, is it possible to get into a good MFE grad school with hard work in undergrad?

Sorry this is probably an extremely basic question but I'm not very familiar with the general field and couldn't find detailed answers online for these specific questions. I'd greatly appreciate anyone taking the time to clear up a few of these questions for me!