I would anticipate that Gatwick to London tickets, ie any that do not specify a given train operator, would be valid on the GEx. It is still a franchised, "normal" train service, and in railway legal terms it was always envisaged that it would be the only routing used from Gatwick to Victoria. Southern and their predecessors coming along later and providing an alternative, cheaper service was never envisaged in the overall plan.

The contractural arrangements for the Heathrow Express are different and they do indeed manage to exclude any ticket types they do not like.

In my experience tickets are always checked on the Gatwick Express, maybe not so much on the slower, cheaper Southern or Thameslink services. In fact on some of the trains used on these routes it is not physically possible as they do not have corridor connections throughout.