I don't see why not. Scholarships do serve a purpose of helping a kid pay for his educaiton, but they also serve the purpose of attracting a player to a school, thereby, in theroy, increasing that school's chances at success. A kid doesn't have to take a scholarship, and there have been wealthy families who have foregone scholarships because they wanted to give someone else that opportunity. This probably isn't at all the norm, but it happens.
And, how would you determine what "wealth" qualifies and what doesn't? Simply AGI on tax returns? Other assets? Do we consider how many children a wealthy family has. Do we consider that though some people may have a good income and are "wealthy" on paper, they may have high debt or other liabilities. There's a lot to consider.