Hi Simon
Southern's website isn't very clear but there are indications within it that travel is only valid between the two stations specified on the ticket. For example, it refers to discounts being available on the "ArunValley (Arundel to Christs Hospital) – London Victoria" route. That seems to indicate that the discounts are only available to/from stations actually in the Arun Valley. (Otherwise they could just say that discounts are available between Arundel and London). Similarly there's a reference to discounted fares as "London Metro area - Brighton". That seems to specifically exclude boarding at other stations along the line, such as Gatwick Airport.
That interpretation of the rules is also consistent with those that applied when I worked on the railways (but not for Southern). Advance purchase tickets are normally only available for travel between the origin and destination stated on the ticket. (i.e. boarding or alighting at intermediate stations is not permitted).
I've not travelled from Gatwick Airport station for many years but I assume that, like most (possibly all?) other stations along the route between Victoria and Brighton, entry to the platform is controlled by automatic ticket barriers. I strongly suspect that advance purchase tickets, with the origin shown as 'London Victoria', won't open the gates.
I'm sorry that my answer is a bit vague but Southern don't seem to want people to know exactly what their rules are! Probably the only way you'll get an exact answer is to use the 'Advance Tickets' query category here:
http://tickets.southernrailway.com/sn/en/contactus
Chris