To the extent it may matter (beyond the school-elitist industries like finance and consulting), it may affect where travel recruiting may target.
Now, a big company with lots of recruiting resources and needs may travel to dozens or hundreds of schools to recruit new college graduates, so the recruited schools go far beyond elite ones.
A small company may not have the resources or needs to recruit beyond the local schools. I.e. it may not travel at all.
A somewhat larger than small company may have a limited travel recruiting budget and may visit a few schools. It is possible that if the one making the selection favors elite schools, travel recruiting may target those schools over others. However, if the one making the selection has other preferences (e.g. larger size, or not willing to compete against finance and consulting, or preference for a non-elite alma mater, etc.), s/he may target other schools.