It that true, though? Does an electronic storage device with full storage have more electrons in it? I don't know enough about how modern memory works to say for sure.
But in any case, you would be measuring the mass of electrons and not the information they represent. This theory suggests that a storage device would have additional mass dependent on information content, so things like whitening / encryption would not matter.
However, here is a question that immediately occurs: If I have a message with "informational mass" x, and encrypt it, does the encrypted message has the same informational mass, or is the mass of the encrypted message the same as a random message of the same length?
In that case you do not have to account for the electron mass at all.
I can see this discussion go very far into metaphysical. :)
I don't have a clue, I just think it's a relevant question at this point.