I experimented with this as I added to enigma_engine.php self-encryption, if no valid key was found for the receiver.
So, I appended a message before the encrypted message, saying that, if he cannot read it (because he does not have the pgp key), he can click on a link which would decrypt the message, if he knows the password.
Now my sieve configuration broke and I am unable to test until I fix it again. But I saw that enigma was behaving correctly. The message was displayed before the decryption password was entered, followed by the ---PGP PART---. Once the password was entered, the message of course disappeared. Same behavior in enigmail.
For my use, I would mark this as resolved. If there is some other use, I don't know.