The Caledonian Sleeper has the worst timekeeping of any train service in the UK. (Actually, with the nonsense at GoVia/Southern, I suspect they may soon lose that title). This is not to throw mud at CS. They run a very complicated operation, where trains join/split at various points. There are an awful lot of interfaces that can pick up delay.
Your appetite for risk might be different to mine, but there is no way I would use the sleeper to get to a morning flight from Gatwick. Get the "normal" Virgin train, then transfer to St Pancras (which is a short walk) for the train to Gatwick. Don't take the tube for this leg - you'll walk longer getting to/from tube platforms than just walking it.