I think the corner ones still do. Check by placing something in/on the enchantment table. I'm thinking the 3rd slot, the max would be 30, even if you can't reach it (?not 100% on that?). If it is 30, you're fine.
Do the bookcases diagonal to the enchantment table, blocked off by the other bookcases, still power the table? For example:
(the crafting table represents the enchantment table)
Do the bookshelves on the four corners still send power to the enchantment table, or not? Please and thanks!
Yes, they do.
15 bookshelves gets you level 30, so you don't need one of the 16 you show. Maybe put an anvil there, or - I like to put a dispenser with a water bucket and a button on it; when it floods around the table, you can get low-level enchants because the bookshelves are ignored.
You can also put bookshelves 1 above all the spaces you showed, which can be handy when putting an enchant table in a corner - for example, you can have 8 around 2 sides, and 7 on top of those. Maybe a light in that free space.