The short answer is no. A layout is a display object in FileMaker, not an independent data entity you can stick into an email.
However, what it sounds like is you want to have a report as the body of an email (perhaps with the current status of a particular record). This is achievable in a number of ways:
1) Create a PDF of the information and attach it to the email.
2) Create HTML mail and distribute it via a mail plugin (or perhaps an email aggregator like Mandrill).
3) Create a web page with that layout and embed the link in the email (again, HTML mail required).
I don't understand the second part of your question. Any script can be used in WebDirect (barring non-compatible steps). But you can create server-side actions that work perfectly well on WebDirect.
Perhaps if you described what you're trying to do instead of how, we could give better advice.
It’s a Property Database and I have to put the Property Move Authorization (PMA) form on the web so users out in the field can use it. The PMA has to be sent to several other employees who need the information. The Manager of this group would like the PMA embedded in the email instead of a PDF attachment.
You're expressing two different issues here. One is web access to the form (which you can achieve via WebDirect). The other is, essentially, a "picture" of the layout (presumably with data?) embedded in an email. The only way to do that, given the desire not to use a PDF, is to use HTML mail and code the form, sending it via an HTML-capable plugin or service.
@Mike_Mitchell, FileMaker does not support HTML emails? I have not tried but I assumed if the body text is HTML it will send and display as HTML.
Nope. Comes across as markup.