The D1 coach is right. The bigger the name - the better chance you have of getting drafted and getting a bigger signing bonus.
But you have to actually play the game first.
I can tell you countless stories of big-name players from big-name schools - that got drafted - played like **** - and then got sent home.
Your focus should be on playing alot, performing well and winning.
If not - you probably wont have to worry about draft money - regardless of what school you go to.