I don't think, or at least don't interpret it that way, that the value of these really has anything to do with the fact that they once belonged to the NYC Board of Education. Rather their value is in their unique configuration that only seems to exist within these few batches that were special ordered by that school district. So that is their identity and identifier, but not the actual reason they are valuable (which, as with most things, is because of limited supply and demand that outstrips that supply).
I would feel that an unmarked example would be worth the most on these as long as it was obvious that it was built in the 1960s or 1970s. Unmarked drums would be closer to mint than an engraved one and also rarer (most seem to be marked in some way). Although, as few and far between as these seem to be, ANY example would be worth snagging if the price is agreeable, marked or not. I just feel that an unmolested example will probably have a bit of a premium attached.
My opinion anyway, I don't think most of us covet one of these because it used to be a school drum but rather because they are a particularly unique version of a good sounding and quite popular snare drum.