Can you ask a school what the profile is for a group of entering students to a COE graduate program?

So, here's a scenario I've been thinking about: My daughter may want to go to a 'prestigious' school that we simply can't afford. If she plans to go to grad school to follow up her BS in an engineering field, I would like to know where the current grad students in her potential program (at her target school) are coming from to make sure she will have a chance. I would rather spend the money on grad school if she's going to go. Also, would they take into account the fact that they accepted her for undergrad, but she did not attend? Or would that be a strike against?