I think it very easily could. Email bodies are often MIME Multipart messages [0]...

I think it very easily could. Email bodies are often MIME Multipart messages [0], which can be nested to arbitrary depth. You can see an example of such a message here [1]. The PGP setup used by default with Mutt will encrypt your cleartext multipart message (which contains your text, html, and attachments) and then send only the new cyphered body.

[0] http://www.w3.org/Protocols/rfc1341/7_2_Multipart.html

[1] http://msdn.microsoft.com/en-us/library/ms526560(v=exchg.10)...

I'm not saying that End-To-End does this, just that it is perfectly possible (and common) to encrypt the whole message.