People will still die even if everyone gets the treatment. They'll die from war, accidents, and diseases. They'll still have heart attacks and get cancer. I suspect even if you completely "cured" aging at the cellular level the average life span would only go up by a few decades.
Consider cancer. The human body has multiple overlapping systems to detect cells that have gone bad. It doesn't cure them, though. It kills them. One of the reasons cancer normally (not always, but normally) strikes in old age is likely the systems which detect and kill cancer cells have been shot full of holes by... the systems that detect and kill cancer cells. That's not going to stop. Your odds of being a cancer victim (albeit more youthful looking) in your sixties and seventies probably won't change very much.
There are other problems that youthful cells won't help with. The heavy drinkers and drug users are still going to drop dead by age 50 or so. Women will probably become infertile about the same age they do today. Morbidly obese people might live a few extra years, but probably not as long as thin people today (statistically).
Actually extending human lifespan appreciably is going to require far, far more than addressing cell aging. So fear not! You're still all gonna die.