If Illustrator has that functionality, I've never heard of it.
However, I do what it sounds like you want to do all the time. I use Outlook email so that's the only detailed description I can offer, but you can accomplish the same with most any email program and the steps will be very similar.
With Outlook, you start a new email and select "Insert > Picture > From File". This adds your image to the body of the email (instead of as an attachment). Right click on the image and select "Format Picture" to scale it and whatever other layout functions you may need. Then, select the image, go to "Insert > Hyperlink", type in the URL (or email address) and you're done.