Is it possible to delete whole Boards??
Yes, it is, and has been done in the past for various reasons, mostly of the technical error variety, though not all of them have been.
Should it be done??
Depends on the reasoning behind why it's being deleted.
For all the reasons that the Mods and Admin can delete posts, they can use the same reasoning to delete Boards. In this case, no, I don't see a valid reason to delete an entire board. There is no objectionable material in it. There's no record(s) of fighting or wars between people. Etc, etc, etc. (Or, as Missy likes to put it, "Yada, yada, yada, Mama."
And while the Shades Board doesn't get a great deal of use anymore, it does hold a world of information to new people (as Sultry mentioned) and us old fogeys who have the memory span of a rotten grapefruit. So deleting all that information might not be the best of ideas. One never knows when it might become valuable again. ;-)
Just a bit of rambling....