I personally dont think why no, but I'll send myself a video and report back.
UPDATE: I recorded a couple second video (5-7 MB or so), sent it to myself via my Outlook account, and I could definitely download and open it. (in the email app)
But nope, the save option was greyed out for whatever reason. (didn't appear in downloads, etc. - I think the email app hasnt been updated to reflect the more file-friendly nature of 8.1, etc.)