You can certainly insert video embed code into the HTML of an email template however most email clients currently do not allow for videos to appear in emails that are received. The video is typically stripped out of the email before the person receiving it views the template.  
We recommend taking a screenshot of the video player and inserting that image into the template. You would then hyperlink the image to where the video is hosted. This way when they click on the video player image in the email they are automatically directed to the video in a browser.