Well, Miss Minelli, I haven't personally tried it yet. But in terms of a rule of thumb, I think it depends on the image format. Most of the wilder, wider-range zoom lenses such as that Fujinon were probably designed for video cameras, and those come in sizes designated somewhat arbitrarily as 1/3-inch, 2/3-inch, and 1-inch.
According to a chart I found on a RED camera forum (and linked somewhere in another thread) lenses designed for 1-inch video should cover at least most of the G1's sensor; 2/3 and 1/3 are quite a bit smaller and I suspect you wouldn't get much coverage out of them.
Another potential quirk: At work I used to use a broadcast-quality video camera as part of an image-capture setup. This was a JVC KY-210B, which was considered quite a nice little camera in its day. It came with an impressive Fujinon zoom lens. The instruction manual for the lens stated that the back-focus distances of video cameras are NOT standardized, so when installing the lens for the first time, you had to align it to that specific camera body via a set-screw-secured adjustment collar on the lens. Presumably you might have to do a similar procedure to mount a broadcast lens on your G1 and get it to focus to infinity.
Another unanswered question: Is a zoom lens designed to give good results on the relatively undemanding format of 525-line, standard-definition video really going to be sharp enough when used on a 12-megapixel G1? This point would make me cautious about shelling out big bucks on a broadcast zoom lens unless I had a chance to try it out first.