If I reconnected my PS3 post-store update, would I still be able to download God Hand or Fatal Frame?
For now, you're fine. The October 19 shutdown only affects the webstore; the PS3 itself will still have its own storefront that can purchase and download games, and so far Sony hasn't shut down the Download List functionality even on the PSP.
Where this gets hairy is that a) the on-console storefronts suck, and b) some games that should be purchaseable on the Vita aren't because of weird reasons, meaning you'll NEED a PS3 to buy those games after October 19/28 (or whenever the old mobile storefront shuts down).
Also c), it'll become a lot harder to backup your PSN purchases because you won't have the webstore's download queue; you'll have to individually download and install every game one by one via the storefront on PS3, even if you use background downloading for everything. I'm doing it now and it suuuuuuuuuuucks.