TCM, you've come to the right man. Yes, yes and no I don't think so.
I'm pretty sure the Gatwick Express is a premium service excluded from cards and offers - but check with the company, i'm not totally sure.
If you take it the Gatwick Express runs from Victoria, every 15 minutes and takes half a hour. If you choose the standard service it takes longer but anything on the Brighton line WILL stop there. However as another option Three Bridges is in Crawley and much closer to the ground for a quick Taxi hop.
If you do stop at Gatwick and want the right bus take this short cut >>>>>> exit Gatwick station via the main ticket hall and head in towards the South Terminal but turn right as if taking the shuttle to the north terminal. Walk right down the Shuttle 'platform' but take the stairs at the very end. When you exit the stairwell at the bottom turn left and it brings you out on the Crawley bound side of the A23 at the 'local bus' stop. It saves a trek as if you follow the actual signs to 'local buses' it'll bring you to the wrong side of the A23 and you'll have a long walk via an underpass to get there.
Personally i'd recommend Three Bridges, there's a huge taxi rank and it's a only a five minute drive through Tilgate. Putney is spot on changing for Crawley but unless you want to kill time in a souless concrete Town Centre you might just as well pay the taxi-man.
EDIT - OOH just remembered........a tunnel became structually in-operative last weekend and there was a bus service between Crawley and Gatwick, it's not impossible they've delayed full repairs until this weekend to minimise disruption to the commuters CHECK FOR SCHEDULED PROBLEMS ON THE SOUTHERN WEBSITE. If so you'll all need to get off at Gatwick and follow the above instructions, the rail replacement buses were a disaster!.