To be a JW, you have to be really good at believing in ideas that completely contradict/oppose each other all of the time.
For instance: A friend of my MIL is 85 years old. She will tell you how horrible this system is -- the gays, Putin, Trump blablahblah. Worst time ever to be living. She will also tell you that the new system is just going to be so amazing. Can't wait.
Funny thing is though, her heart is failing and instead of letting nature take its course and leaving this horrible, awful system behind and stepping into a panda-petter's paradise, she has travelled from Florida to NY several times to receive experimental treatment/operations for her heart condition. So does she really believe there is a new system? If she did, why would she be doing this to preserve her life in such an awful "system of things" for a couple years?
So back to the OP: Do they really believe they are living in the time of the end? I honestly think the answer is both Yes and No at the same time.