Who you know if far more important than what you know. This is true, like it or not. A very close second is your attitude.
My personal opinion to the original question? No, I do not believe it matters what school you go to.*
*HOWEVER - I also believe strongly that the best people in aviation are the ones who are self-motivated and driven for success. You have to approach your basic curriculum just hopefully like you would with the job you'd like to have, and that should be with an attitude of "I want to learn everything I can now and later in order to do the very best job that I can; I know people are depending on me and I care very much about not letting them down".
Using this attitude to pick a school, are you going to pick a place that 1) guarantees everybody passes, no matter how unqualified/unintelligent/shouldn't be anywhere near operations they are, 2) doesn't teach you everything you need to know, and 3) doesn't hold you to any real expectations? Doesn't sound good to me - don't waste your time and money. Sometimes the easiest road ultimately is the bust-your-ass road, because it's going to open up opportunities for you, not the "gimme" road.
Another point, THERE ARE SOME TERRIBLE DISPATCH SCHOOLS OUT THERE. How they stay operational is baffling to me. The FAA takes awhile to shut down shops, evidently, or they are just completely looking the other way. I have personally seen their "graduates" from a couple of these places on the job and their performance ranges from moderately just ok to a complete disaster. All of us are brought down by these people.
To be truthful, I have also seen great people from more than one school; what they all shared in common was the drive to be the best. Innate abilities and results account for something sure, but it's not everything. Be smart about your choice because many of your competitors for the job you want chose the bust-your-ass road, and continue to do so after they're hired.
Summary: Just do yourself a favor and go to a good school. It's pretty much the same price (or cheaper) and you're giving yourself a good framework. Please don't give any money to a clown school because I would like to see them all dry up and go away.
Living and personifying the attitude of "I will make it happen" virtually guarantees eventual success. People will notice and you will network. Opportunities will come because you've made them for you and you stand out. There are many good examples of these people who post regularly right on this website. Don't even need to mention names, they stand out on their own.
Just my .02 everyone. Good luck.