Yes, that was the pub before it burnt down, and Hogarth did indeed spend a very debauched weekend there back in 1600 and frozen to death. The new building is the age I stated above.

If you are into Hogarth, while you are here it may be worth visiting the Hogarth Arms on the Isle of Grain a few miles down the road (overshoot, landfall is Zeebrugge) and the church there too.