While this may stop aging (assuming it works in this scenario), it won't stop things like car accidents and murders, and probably won't stop things like heart failures, strokes, cancer, starvation, and obesity related deaths. Obviously there will still be a large number of people who would have died of old age who will no longer die, and this will change how a lot of things work (like social security, pensions, and such), but it probably won't cause an explosion in the population, just a higher proportion of tragic deaths.
It could do very interesting things with the way people live though. If a bunch of people retire at 60 with stable investments and a youthful body, they could do all sorts of things for the next hundred years or so.