"big" is relative. I went to a private UG school that had about 400 - 500 people max, so 6,000 to me does seem big. But in terms of applying to b-school, no, it's not that big.
My point is that I think which UG has less to do with admission to b-school than how well you do while there. I would like to see the % admission for some of those top UG school. This would help the argument made by another poster that those top schools are going to be more selective to begin with, so the pool of students will be more talented and more likely of success from the beginning.
I think a good experience at pretty much any UG institution is going to say something about the applicant. Even if it is a "party" school or somewhere not known for strong academics, if that person comes out with a BS in Engineering and had a 3.8 GPA, and tons of extra cirricular activities, the adcoms are going to see that this person was active and a leader. That is what I believe adcoms are interested in.
It's not so much where you went, but what did you do while you were there? If you had no interest in making your UG community a better place because you went there, how are you going to make our b-school a better place because of your attendance?
Most successful people are successful because it's something inside them. I've seen plenty of people born with a silver spoon and handfuls of opportunity only to accomplish nothing. Adcoms want to find the people that succeed and do so regardless of circumstances or obstacles. That is why the essays, work experience, and leadership roles are so important.