There is not really a way to do that but you can make a video with a screen recorder and send the video or give a link to the video or a link to your comp if you have a server to host it.
Is there a way to convert it to an animated gif?
you could also try this. From EA, goto Publish settings and turn on > Animate deployment package. This creates a single file, dont forget to make a poster image (preview snap). Once you select the path and hit 'publish' EA will create a single OAM file which you can then create an html page in Dreamweaver and place this 'oam' file inside. here you can test and see your animation work when you preview it and send as email.
You can also try MS Word and there is a way to send an email direct from Word using your email client like outlook etc. you have to add the command 'send as mail recipient' to your toolbar.
This is just a pointer for you as an alternative but otherwise you could try the above suggestions also