The airport will not be deserted at 0630. It shouldn't be over run either, but don't assume you'll be the only one using it.
I can't see the point of going to Victoria to pay much more for train branded Express when you have cheaper options from a station closer to you (Blackfriars). If there is the remotest bit of disruption it is trains branded Express that get canceled first (the opposite of what many people assume happens).