If you have already shut down, there is unlikely to be any leftovers from any in-memory copies of the contents gedit was editing.
In gedit, there are preference options to create backup files. Look for these options under Edit...Preferences...Editor. If you happened to have turned on the autosave function, you may find a copy of the file with ~ appended to the name stored in the editing location (but in this case, I suspect you would have found it when looking at the FTP site).
In summary, probably not (and you probably already did something else to recover the content in the last 15 weeks), but if you set this option, you may discover that the answer is "Yes" in the future.