Well it would mean new sources to use of course (would they be used though? Even most of the reams of paper documents produced during the bureaucracy booms in the 19th and 20th centuries have never been read after being deposited in an archive...), but there's no reason to expect the actual methods of historical enquiry to alter. Most of it is really just applied logic (or at least it ought to be).
Well, things like textual analysis can be performed on electronic archives but not paper ones, for example. Paper archives also don't have things like metadata. Previously, if I wanted to find the frequency of mentions of a particular politician by date in all publications over a 20-year period, I would have to either manually count or OCR every document and search, then categorize the date of each publication. But that still wouldn't allow me to see which references to that politician appeared in reference to, or because of, another reference.
With electronic sources in structured form, I can simply write a script to gather metadata such as date, time, document type, location, author, etc. as well as trace by sources through hyperlinks, previous conversations by the same profile, retweets, etc. This allows me to more easily make casual relations such as, "This cluster of activist centered around X, Y, and Z organization started talking about Occupying Wall Street before anyone else, and they influenced A, B, and C," and do so in a quantifiable manner.
That may be true of the unstructured web, but I guarantee that companies such as Facebook, Twitter, Tumblr, Google, etc. have stored their data somewhere from almost the beginning of their operation, even if you have "deleted" it. Of course, it's a real question of how much of this data is
accessible by historians or other academics, or whether they'd immediately know what to do with it; but I have little doubt that the data exists, and is accessible by
someone, and it's only a matter of time before it's opened up, piece by piece, and only a matter of time after that before every bit of intelligence is extracted out of it, by people who do know what they are doing. I wouldn't be surprised if a script 80 or 100 years from now were to be analyzing this very post I am typing, obtained from Google's (permanent) cache.