Perhaps a better question might have been "How much use would the Vulcan have been in Gulf War One?"
I was told that someone was seen laughing hysterically over the payload-range 'capabilities' of the new bomber which was supposed to take over from the Vulcan back in 1982. Particularly with the engines it had back then. Simply not feasible.
But a proper RN carrier or two with Phantoms and Buccaneers instead of little bona jet boats would certainly have made a considerable difference.