You need it hooked up for sure while it's carbing up. Then when it's dispensing if you don;t leave it hooked up it will slowly loose pressure and carbonation as you dispense.
I'm putting 30 pounds on my keg and then disconnecting to carb up. I started on Friday and today Monday I'm drinking some undercarbed but still good beer. Another day or two should do it. In the meantime, my picnic tap broke and I have trouble pouring anyway. I think another trip to the LHBS is in order to get a replacement, and maybe I need another batch while I'm there
Like zacster said, you can up the pressure to 25 or 30 psi and "force carb" in about a week then drop to serving pressure,or leave it at serving pressure( 8 to 10 psi for most) and let it go a couple of weeks.