I think you can get recognition coming from a smaller college, you just need to work that bit harder to get your work seen. Colleges like CSM get a lot of press, and so it's often easier to make it in, say the fashion industry fo example. That's not to say bigger is better. I studied at CSM, and it has it does have it's disadvantages. I guess it's often easier to stand-out if you study at a more low profile college.

I`ve been on a quite small and totally unorganized college. This means no connections to other institutions or organisations and because of that almost no public appearance of the work. But the profs were really ok, as well as the quality of the work, because they had more time for everyone. I think quality matthers and you have to make yourself heard. There are a lot of possibilities like competitions, awards mags ect.

I went to a small college with some really poor staff. So I went out and educated myself - I learnt more working for nothing in a designer's studio than I did at college. And it doesn't have to be a big name - it's often better to go to a small, up-and-coming designer. They're more grateful for your help and you get more opportunity to do more than sew or cut patterns, not to mention making contacts.
I know it's hard to work for nothing, but I did shifts in a factory to support myself. The short-term sacrifice was more than worth it.
I also took advantage of what my college did have to offer - other creative minds. Painters, philosophers etc. all helped me to expnad beyond the narrow fashion rut.