I wish I had a better response for you, but the answer is no.
The image is not actually embedded into the signature. It is called into the message/posting at the time it is displayed, in this case, as part of the e-mail message.
If you were to call it from a fixed drive location, it would cause an error when being displayed outside the local network. Therefore, the image must be called via a public URL for the signature to properly populate the image from anywhere.
As an FYI, if you have the user's information populated into their contact, you can use the variable dropdown to build the signature and then add the image at the appropriate place you want it to appear. IE:
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