If you don’t check the box, then you can get in to either Harvard or NEC but they won’t have evaluated you for the double degree. A student can apply the next year, but not checking the box makes it hard to get in for freshman year if you later decide you want to be in the double degree program as a freshman.
I think students are mainly considered for the double degree at Harvard, based on musical talent and accomplishment, and, obviously, ditto on the NEC side.
Harvard and NEC evaluate candidates as if they only applied to that school, I believe. Consideration for the double degree is separate, and of course depends on admission to each school first.
In general, high level music at Harvard is a “hook.” It isn’t that candidates who do music are evaluated differently the way a school with a conservatory might do (with conservatory faculty at, say, Oberlin, advocating with college admissions and financial aid). But Harvard wants a mix of student interests and abilities, so music helps. It is all about the class, and the ability to contribute on campus, in that sense. A student might have a better chance to get in with grades and scores a little lower, with high level music ability and achievement.
NEC welcomes students to the double degree program. I cannot speak for individual teachers at NEC and their attitudes toward the double degree, but I have never heard of any kind of negative reaction or experience due to NEC thinking Harvard students are less committed to music. I am sure the presence of these students broadens the experience for everyone.
The double degree program benefits both schools. However, students are screened for it and “only the cream of the crop” do it. If a student is not admitted to the double degree program, he or she still may have a great shot at getting in to both Harvard and NEC and can try again the next year.
One thing to think about is whether NEC is in fact where the student wants to get a master’s. That extra year can mean quicker entry to a PhD or DMA but some students might, after 4 years, desire a different location for a master’s. Also the double degree includes a fee of what used to be $6k even for kids on Harvard financial aid, I believe, so it is expensive, and students can always take private lessons instead.
It is also worthwhile to point out that Harvard started focusing more on applied arts in recent years, and now gives credit for lessons and performance in certain ensembles. There is also an undergrad composers’ collective that holds concerts with both student and professional musicians.
I cannot entirely vouch for anything I have written I would want anyone reading this to check on the websites and to ask admissions and/or the relevant department these questions. A tour of NEC can be very informative and the music department is available at Harvard too.