I would say no, though my usually answer of you can do whatever you like also applies. But I really do think a wedding invite should arrive in someone’s mailbox, and not in their inbox.
Save-the-date cards, in my opinion, are fine for email, but make sure granny and her generation get a hard copy, or at least a phone call, if they don’t have an email account.
If you’re making a green statement by emailing your invitations you can also make it with a wedding invitation that is made from recycled paper or cotton and uses eco-friendly inks. A number of wedding invitation companies are eco-friendly including Oblation Papers & Press and Crane & Co.
Another e-invite don’t is the emailed RSVP. Maybe I’m old fashioned but it’s appropriate to include an RSVP card and envelope set for guests to send their replies or you can send an RSVP postcard and save on the extra printing and a few cents on the stamp.