Will Dreamweaver email template allow for MP4 video to play inline

In theory, some email clients do support animated gifs. So depending on what you want to display/achieve you could add a animated gif in the email. It will fall back to non-animated for non-supporting clients. But be aware of the filesize and probably some clients block the image or will mark the mail as spam more likely (one of many factors).

What about showing a preview of the video-player (screenshot) and let people click on the image that then opens the page with the video in the browser? That’s how many big companies and/or marketers solve this.

Email is text-based communication.  Nobody appreciates being sent bandwidth heavy files via email. That's a terrible thing to do.

If you want to share video, post it on social media or upload it to DropBox and send them a link.  Let them decide if they want to consume it or not.

For an incredibly small percentage of people who are both using a video-enabled email client, and whose security settings allow automatic download of remotely stored files, all you need to do is add an HTML5 <video> tag to the html of your email and link it to your file online.

For everyone else, there's really no way to do it, their email client, browser and/or security settings won't allow it.