In my experience (which, in fairness, is mostly evenings and weekends), the ticket barriers on the SouthEastern platforms at St Pancras are almost always closed, and frequently "set up" (if you'll pardon my potentially incorrect understanding/terminology) to reject all manner of tickets which may require further checking, e.g. railcards - to the point that on occasions, I'll aim for the manual gate to save trying to elbow my way back out of the building queue behind me.
Only the OP will know if they are used to seeing this on their regular commute, but SouthEastern may well question any plausibility of purchasing "as I was getting off", rather than earlier in the journey, as indeed they might any suggestion that Stratford was chosen accidentally for Sittingbourne, given the need to type in a minimum of three characters on their systems, at least, and 11 stations between the two even if picking from an alphabetical list.