Maybe, it's a close call as to whether you'd save much money or not.
If it's just Kyoto and back, then there's a specific discount ticket for that journey here.
Otherwise the price of a 7 day rail pass is a little more than than Tokyo, Kyoto return fare. So you'd need to do bit more JR rail travel to justify the price. Narita to Tokyo and back every day for a week might just about do it since it's ~1000yen each way using a JR train.
Also see our Shinkansen fare calculator.