Probably not. There's a thing called Hayflick limit, which is basically a limit of life expectancy caused by a shortening of telomeres with every cell division. And since most of our cells complete cycles more based on time (life cycle of RBC 100 days), and not due to damages to a cell, our telomeres would still shorten at the same rate. Of course the gravity could play a small part once organs have started failing, but there are many other factors that affect how long it takes for everything to completely deteriorate, and wouldn't have a big role. In fact, it could even shorten life expectancy, seeing as how our bodies are currently built to live in our current gravitational field. Without gravity, our muscles could become weak, causing other problems, which is why people at the space stations have frequent dedicated times to workout, to keep their muscles fit.