I think this would be workable with a few tweaks. First, PDFs should never need a sign off because they should already include the owner's name. Second, the resource tracking sheet should never expire. Third, any GM should be able to sign the tracking sheet; we already trust them to run the game and fill out the chronicles correctly after all.
I think some folks have missed one key requirement, that the player is still responsible to bring a copy of the rules with them to the table, either a PDF print out or a photocopy of the relevant page(s) from the book. So the GM still has the official text to use for rulings.
As far as abuse of the rules goes I don't really see how it would be worse than now. In particular you can change the name on a PDF you didn't buy if you are intent on cheating, which isn't much different than making an extra photocopy of a book page for a friend. The people that would intentionally cheat the rules, such as forging someone else's name, whether on a PDF or a tracking sheet, are probably already fudging their die rolls, "misunderstanding" how their abilities work, etc. I don't think it's a good idea to make honest peoples' lives more difficult because some people suck.
I acknowledge that the time taken to sign the sheets is an additional burden on the GM, but if they don't have time (such as at a convention), they can just ask the player to have it signed at a later date. After all the player must have the resource available at that time to get it signed off anyway so it does not prevent them from playing their character.
I myself was bitten by the removal of photocopies as a legal rules source. I owned everything in hard copy and was tired of lugging it all to every game, so I photocopied every bit of rules I used outside the CRB. Not long after that photocopies were made illegal and I once again had to start carrying all my books to games. That was pretty annoying. I wasn't active on the forums at the time and never saw anyone else in my area using photocopies, so I don't know how much this was truly being abused, but that experience does make me empathize with Gary on this.