I attended selections of three different airlines and i can honestly say that at each of these selections the name of the school was no factor.
I trained modular at a very small school (around 15 students in total) and did my MCC on a B200 FNPTII... in most people's minds i would be the least employable person on the market. Well i wrote three applications, got three invitations to the selection programs and passed each of them up to the final stage. Blew the first one, passed the second and called of the third... At no point had the name of the school any relevance, neither at the selection i failed nor at the one i passed.