No, the iPad baseband can only be installed on the 3Gs, and I am using an official carrier. If you want to unlock you should do it because that's your only choice.
Baseband is the firmware for the modem, without it you would not be able to use your device as a phone. There has never been a way to downgrade baseband except for on the older iPhone3G. Ultimately you would like for it to be downgradable so that you can install an ultrasn0w compatible baseband, but it hasn't happened yet.