Hi David, you don't seem to be getting much response to this so I will chip in. I don't use the email option for sharing replays so I cannot be certain about my answer but I would guess at a no, I don't think deleting the email would break the shared replay links, but to be totally sure I would test it out yourself by saving a replay of any old shot & sharing it through email then delete the email to see if it has any effect on the link.
↓↓↓ EDIT : You're welcome David. ↓↓↓