Mr. Ramsey, I just want it to be clear... as a graduate of the Yale School of Music, I can attest that while, yes, it is under the umbrella of the university in name, it operates (just as the other so-called "professional schools") as a completely separate entity. Obviously I know it is not a conservatory in name, but when you are a student there, you are studying only music. You can spend your entire degree not setting foot in any Yale College building. It is absolutely just as immersive as New England Conservatory, for example.
The big difference is that all the students at Yale School of Music are pursuing graduate degrees. You must already have earned a Bachelor's elsewhere. Obviously getting an undergraduate degree at Yale is a totally different thing. Then, you would not be in the professional school and would have to pursue a more rounded education. But, the graduate program in the school of music is identical in every way to a conservatory.
Anyway, I was just trying to clarify.