I'm sorry, but I don't follow.
For all bit-identical copies of a file, the secure hash will be the same. For all copies of that file encrypted with the same symmetric encryption key, the same property holds. Encrypt it with AES-256 using a shared key, and all users can still take advantage of the LAN copies and de-duping that Dropbox supports for unencrypted files.
Now, if you want full asymmetric (RSA, PGP, whatever) encryption of files with per-user keys and fast LAN copies/de-dupling of the plaintext version, you're of course out of luck. That's not a failing of Dropbox, though; the same would be true of any NAS solution, locally-hosted or not.