First of all, remember that NOT ALL RATES QUALIFY for using points to upgrade. You can't use most internet rates, and in many cases, no AAA, AARP, etc rates. GP can tell you which (more expensive) rates qualify. This is on my list of "The Five worst things about Hyatt Gold Passport". I mean, if someone is going to use his or her points earned by loyalty, just let them be used.....don't punish the person!
That being said.........
I upgraded to a suite with points once, and once used an award for a stay in a suite.
It really depends on the hotel and what you're expecting. For example, I upgraded using points at the HR San Francisco. The "suite" was a glorified king with a desk and a couch. After a discussion with the desk, they gave me the points back.
I used an award in Hawaii (Kauai) for a suite and was put in a stunning room for 5 nights. Then again, Kauai did just about everything perfectly.
You can generally use points to do what you want. If you want it for a week, they'll charge you more points. My suggestion is that you consult with the hotel's Rooms Executive prior to booking your award. Tell him or her what you want, and ask for advice on how to book in with Gold Passport.
The people at hotel level at Hyatt properties, in my experience, have been wonderful, and really care about GP members. It brings you closer than just talking to GP reps who are allowed to follow published rules and nothing more.