When you get to the Hyatt, they'll give you a paper with information about the
DCL transportation and they'll tell you when you should meet the DCL rep in the lobby*. In September, buses started leaving a bit after 9am. Likely, that's still the case. Luggage pickup was at about 8am, but you could also bring your luggage down to the rep in the lobby. Anyway, when you get to the port, you'll bypass the PAT checkers entirely and go through testing, security, check in, and boarding. Your boarding group doesn't matter. Disney doesn't want you idling around in the terminal.
There's probably a wait on the walkway before you get onto the ship, though. The little mini show that they perform for everyone seems to take forever!
* Assuming that you told Disney that you'll be staying at the Hyatt and that you'll be taking DCL transportation to the port. If you haven't linked the reservations, then you should do so before you go.