Nope, they are firmly attached to the belief that human existence is exactly 6,037 years old. They brush off the mountainload of evidence to the contrary by claiming that, while radiocarbon dating methods are reliable back to the flood (about 4,000 years ago, roughly), they cannot be trusted prior to that. Why? Because the removal of the water canopy disrupted atmospheric radiation and so there is no way of knowing what the proportion of C14 to C12 was.
Which is absolute nonsense, of course. There are numerous independent and yet harmonious methods of detecting historic carbon levels, including oceanic foraminafera analysis and ice core samples going back tens of thousands of years, neither of which would have been affected by any supposed shifts in atmospheric carbon levels. But, alas, such independent research and (even worse) thinking is not to be engaged in by the majority of JWs, many of whom just don't have sufficient reading levels in order to process the implications of this kind of research.
But here's another way of thinking about it. Let's say that the WT is right--that at the moment of the great deluge, when the water canopy came down, there was an immediate, dramatic change in radioactivity significant enough to affect the rocks and all fossilized remnants of life. That would create a paleontological/chronological boundary as dramatic as the KT boundary with its iridium layer, which would profoundly affect all dating methods in every discipline and would be very well-known among scientists. Think about it: radiometric dating predictions would function orderly all the way back to the date 2370 BCE, then suddenly, wham! Everything gets funky and the predictions don't work anymore; another model has to be substituted. You don't think scientists, researchers and other professionals wouldn't notice?