My guess is that the isolated outputs help to keep noise down. It's definitely not for surge protection though.
As for plugging in the 1 spot into the Furman- it can't hurt, and is probably what makes the most sense. Is it going to be any quieter than plugging it in elsewhere? Maybe a little tiny imperceptible bit, but it most certainly won't be a night-and-day difference. There is really no such thing as a magic bullet for bad power quality. Sometimes you just have to work with what is there. You can ground lift and power condition all day long, but sometimes you just have to live with the fact that whenever the refrigerator down the hall turns on, there is going to be a buzz everywhere.
From a noise perspective, the biggest benefit you'll ever get is by putting as much stuff on the same circuit as you can. Long story short- one of the places electrical noise can come from is differing voltages to ground. In a place with bad wiring, you might have slightly different voltages for each different phase of the incoming power. If you put your amp on one circuit, pedals on another, the guitar player does the same thing, and the PA is on yet another circuit, the result can be a very noisy system. If you can put all the backline amps on one circuit (or at least circuits on the same phase), you'll have as happy and quiet a system as possible in that venue.