I think that it depends on if they are a senior in high school that is going to be a freshman at the school or if he has been there for a couple of years. Some universities have different marching styles/techniques that are different than what high schools do and as an incoming freshman I could see the importance placed on the student for needing to be there. However, if they are a junior or even sophomore for that matter and know the drill and know the way things work then I don't see a problem with them missing.
Where I went to school, if you were a music major you were allowed to miss any days of band camp/leadership camp due to drum corps (typically it was just 1 or 2 days). For those who weren't music majors it was as easy as being an adult and talking with the director. I think some college (and high school) directors get a 'sour taste' of drum corps because of the way kids approach the directors about it and have an immediate negative attitude when they are initially told "NO" or "You will lose drum major, leadership position, scholarship, etc." by the director. Finding a solution on both ends is easily do-able just as long as the student is willing to work with the director(s).
As far as the scholarship is concerned, it seems like a solution of being in another concert ensemble or helping out with rehearsal set up or some other band-related activity could suffice enough to make up the week or weeks that they missed for drum corps.