The Canon IS system is entirely contained within the lens. Canon has two classes of film bodies, I believe they refer to them as "Type A" and "Type B". I don't remember which is which, but vast majority of film bodies are of they same "Type" as the 1V. A very small minority of (very) old bodies may not support IS functions.
I've happily used a 1V with a number of different IS lenses, including the relatively new 100mm IS macro. I've even used IS lenses with a Rebel G (purchased in 1997). So you're definitely OK with a 1V.
The only thing that film bodies *can't* do is take advantage of the advanced AF processor in the Series III teleconverters along with the series II super-tele's, but the AF function of the body and the IS function of the lens is retained.
--Greg