Here's my view. I'm more of an intermediate driver rather than a pro, but I am an avid tracker:
I'm personally happy with either transmission, and I believe that you don't need a DCT auto to take the Ring record. I think that it may help, but it's contribution would be smaller than other factors such as better tires, big active aero, brakes, and who knows what else.
But the reality is that a large number of candidate Viper owners are already driving DCT trannies, and if SRT wants to capture that market segment, then they need to get one in the car. That said, there may or may not be budget for it, and there may be issues getting one to fit in the Viper as some have pointed out. I'd personally opt for the stick shift, especially of a DCT is a pricey option.
Either way, I'd buy an ACR in the future. But people like my friend Mike who has owned Ferraris, a Lambo and a Porsche Cup Car want the DCT. He drove my Viper at Laguna Seca a few weeks ago, and absolutely loved it. He said without question he'd buy one if it had a DCT. His case may be more unique than others, he has a knee that gets aggravated from clutching, although he can heel-toe with the best of them.
To me it's less of an issue of taking track records. To drive sales, the Viper needs a DCT I believe. Not a crappy slush-box auto like what's on the C7 (Mike drove one on track and said nooooo waaaaay). A true high performance auto like a DCT.