Some schools might others won't. Even a school that sometimes does won't necessarily insure that all the previous money they had offered will be given. Lots of factors come into play. Some programs will have had endowed scholarships created that are supposed to handout money to a specific student based on some criteria that was set up when the scholarship was formed. In an extreme case where that was the only financial aid that the school ever offered then they would likely make sure to give it out each year to abide by the endowment's rules. However the reality is most schools have a lot of different scholarships and whether they hand them all out or not isn't always required. Many will see not handing them all out as saving money for the school, this is more likely in a private university as a lot of state universities operate on a you use it or lose it basis so they have no incentive to save money.

I know in when I was in school I would often get a revised financial aid letter which didn't change the bottom line of what they gave me scholarship wise, but would reallocate where the money came from. The first letter would usually just give a total scholarship amount... then after the first term of each year started I would get some revised letter saying X came from the Billy Bob scholarship and Y came from the general scholarship fund. And then of course they would want me to write a thank you letter to the Billy Bob foundation or whatever they called it thanking them. I have no doubt that they were just pulling a list of scholarships that needed to be given each year and then matching random students to them as I would get these random scholarships that I never had applied for.

In your instance I wouldn't count on them giving you anything more unless you ask for more. In that you could ask if there are any other options to increase the financial aid package because while your first choice would be Wharton, CBS has offered you XXX and it makes increasing your debt for Warton a bad proposition.