Can Safari on an iPad be controlled with gestures?

Solution 1:

Yes - Dolphin Browser supports gestures. So do Atomic Web Browser and Perfect Web Browser.

As you correctly realised the answer is no for Safari, unless you count the four-finger swipe up to get to the current app list, and other system gestures.

Solution 2:

There are a few Cydia packages which modify Safari to enable gestures and fullscreen mode. I have used "Fullscreen for Safari" which kind of works but is buggy with the debug console enabled (and the swipes are also buggy) on my iPad3.

I have also tried "Swipe Safari" now and it is far superior to the other one, though I think it costs more. It gives you a lot of options in terms of gestures (one, two, three finger swipes, pulling, multi taps, tap and hold)