Other defendants suggested the answer was no.
An html application, on the other hand, is likely to open in the environment in which Javascript is running.
EDIT: It has been suggested that I did not answer this question properly, so a more complete effort is being made here.
Summary. I expect that many or most users receiving an html-formatted email address containing embedded Javascript will see that it is running and have tested the tests to make sure this is true in some environments. But Javascript will be blocked for some users.
Protocols (in particular, RFC2854) explicitly address scripts (in text of type text / html) with the statement that:
In addition, the introduction of scripting languages and interactive features in HTML 4.0 have introduced a number of security risks associated with the automatic execution of programs written by the sender but interpreted by the recipient. user agents executing such scripts or programs should be extremely careful to ensure that untrusted software runs in a secure environment.
So, the protocols support Javascript, but what user agents do?
My (ancient) email reader uses a spreadsheet to indicate which viewer software to use for each mimetype type, diverting html content to my favorite web browser. Almost all current web browsers support Javascript (and some of them cause terrible warnings when trying to disable it!). Modern email agents have internal html interpreters, and if so, is javascript turned on or off? I checked the Thunderbird documentation and found that javascript is enabled by default but can be disabled: http://codeverge.com/mozilla.support.thunderbird/simple-html-tags-reference-docume/2030160
I noticed that some (???) users now access their email directly from the browser (webmail is one such platform) instead of running separate email software. All such platforms that I have tested so far run any Javascript embedded in html email messages. However, some of these environments, depending on the user's security settings, do not automatically extract external links (Javascript or images or others), so it can only run external Javascript from a file that is included as an attachment to the message. The same can be said of any standalone email reader on a device without a current Internet connection.
The above applies to javascript embedded in the body of the message in the email element. You can also specify html explicitly as an "attachment", which, if it is saved and then opened, will be displayed in a web browser, where Javascript is available with a very high probability. Thus, it would be possible to include a second copy of the javascript-enabled message as an html attachment with an alternative text / plain main body and / or tag in the main text / html directing the user to the application.
I thought about it because some of my friends insist on sending me "greeting cards e-mails", which consist of a text message directing me to a link that I found so unsatisfactory that I refuse to even consider downloading it simply by principle. I wrote and emailed greeting cards with interactive graphics, music, and even games using the built-in javascript and was satisfied with the result.
Therefore, I affirm that the correct answer is “Yes”, both on the grounds that the protocols are specific to the scripts and that all mail agents that I personally used run Javascript in my test emails.