I'd be worried about doing that. I know you said it worked for someone in the past, but unless they went to some sloppy school that couldn't figure it out, especially if it was something you had to coordinate from a distance, I wouldn't mess with this. If you do, I would attempt to have it done properly first and do this as backup several days later. It doesn't hurt to send multiples. It just shows up again under transcripts (as an AU).
I would rather risk it showing up without the matching form than showing up with the form but having the envelope from the school addressed to me. So maybe doing both is a good option so you're not relying on just the one. They'll match it up. It's not going in the trash.
I think your schools can handle it though.