I've been doing this for a long time. The mail will be rejected both internally and externally.
There are several snags, though...
1) If she's on any Distribution Lists, the senders will get NDR's for mail sent to her mailbox (this may be annoying)
2) Brick level backups on that user's mailbox will fail and may cause your backup utility to report failure. If you're only doing DB level backups you will have no problem.
3) If the user is part of any Internet Distribution lists, she may be removed from them because NDR's will be sent back to the senders (Unless you have NDR's to the internet disabled)
PSC
Governments and corporations need people like you and me. We are samurai. The keyboard cowboys. And all those other people out there who have no idea what's going on are the cattle. Mooo! --Mr. The Plague, from the movie "Hackers