Can you go through 4 years at USNA and still not recognize some of the people you graduate with?
PMJI, but absolutely. This is more true if, as in my day, you stayed in the same company for your entire 4 years. You know the folks in your company incredibly well. You know folks who were in your PS company (two other companies next to yours -- e.g., 4, 5, 6) pretty well. Depending on the # of mids in the major, you know those folks from pretty well to very well. You know very well people who are in your sport and/or ECAs. You also meet a few during summer activities. And, in my day at least, all of the women knew each other by name and by recognition.
However, there are ~1150 in a class. Folks who are in the other regiment ("other side of the world") and with whom you don't share activities . . . you don't know them and, in some cases, may never even meet some of them.
With "shotgunning" or "scattering," you obviously get to know a lot more folks in your class and in the brigade as a whole. This is one of the arguments in favor of doing this.
So, for example, at reunions, I frequently run into people I do not recognize/remember at all. That said, there is also an immediate bond. We will find some shared memory or event or something that allows us instantly to engage in great conversation. It's one of the unique things about the SAs -- the bond you have to your classmates, whether or not you knew them well or at all.