You can't.
It's unfortunate, because there used to be a workaround using Picasa (details below), but it no longer works.
This is all moot anyway with the move away from Google+ Photos to Google Photos. Google Photos doesn't have an email option either, but there are other ways to automatically get photos in there.
The steps below no longer work, but are left as a legacy.
It used to be possible. The key is that you don't do it through Google+, but rather Picasaweb (soon to be Google Photos)
- Go to Picasaweb
- Click the gear in the upper-right corner and select "Photos settings"
- On the "General" tab, there is an option for "Upload photos by email:"
- Click the checkbox and select a "secret word". The combination of the secret word and your user ID will create a special e-mail address (i.e., {userID}.{secret}@picasaweb.com)
- Use that e-mail address to e-mail images to your Picasaweb (and, thus, Google+) photos
![Picasaweb email options](https://i.stack.imgur.com/8EjzU.gif)
The photos appear in the "Drop Box" album, which is the default for newly uploaded photos, and the e-mail subject is used as the caption.
From here, you'll want to move the image to an album you're already sharing or, if you want to share every image you send via e-mail, you can share the Drop Box album with whatever Circles you want and it'll appear in your Stream.
Note: Google recently changed picasaweb.google.com
to redirect to your Google+ Photos. While they do provide a link to get back to Picasaweb without redirecting there's no telling how long they'll keep that link around. There is not, at this time, a way to upload photos to Google+ via email.
There is a story about google's ID verification I read just this morning that would be relevant to your question. It seams that if people report your name as fake or for impersonation, a simple photo ID scanned and emailed is all you need to get back on course. As it turns out in the story, even a fake photo ID will pass the test and get your account a green light.
Best Answer
No, it is not possible. Takeout links with your Google+ account, but Google+ does not has any connection with Takeout.
Google+ does has an API, but there is absolutely no way any API would ever allow an app to alter it's user personal details.
Also, a single person creating and using multiple accounts, or someone creating an account with the exact details of an another account is something no company had ever wanted.