Yes, many people reached old age in the pre-modern period, regardless of what date you use for "modern" (okay, maybe not if by "modern," you mean modern humans, i.e. the evolution of homo sapiens). Life expectancy data is heavily skewed by early deaths in the pre-modern period, though to be honest early deaths also skew current life expectancy statistics, even in developed nations. Without modern medicine, very early childhood (birth to about the age of 5) is very dangerous. Later childhood (5 to about 10) is also pretty dangerous. Because so many people would die so young, that drastically lowers life expectancy. If a third of people die before the age of 5 and everyone else died at 60, the life expectancy would be roughly 40-42 years. If half of people died before the age of 10 and the rest died at 70, then life expectancy would be roughly 35-40 years.

The second problem is that there's a second spike of very dangerous ages for both women and men. The biggest danger here was childbirth. Bearing a child is still a dangerous proposition for women, but without modern medicine it was very dangerous. As such, you see spikes of women dying as they reach childbearing age. In addition, lots of men died (and a significant but nowhere near as high a number still do) as adolescents and young adults due to violence, whether it's war, banditry, or urban violence. Even in periods of relative peace, lower levels of state control would mean more outbursts of violence and that usually draws in lots of young men. At a certain point, men age out of being involved in organized violence. This means you end up with a lot of men dying from the ages of roughly 16-30. So, in addition to lots of people dying in childhood, a lot also died as young adults due to violence.

So what we see are large spikes of childhood deaths, significant spikes in women's deaths during childbearing years, and spikes in men's deaths during the when men are most likely to engage in organized violence (by choice or compulsion). This skews the data significantly. Generally speaking, if someone can avoid dying before the age of 5, and then avoid dying in childbirth or war in their 20s, they could live to what we would recognize as old age. Now, this doesn't mean everyone was living to old age who survived into their 30s or 40s. People still tended to die younger, especially poorer people, but plenty still reached old age.

Also, I suppose it depends on what you qualify as "grand old age." I'm assuming you mean surviving into their 70s and 80s, which many people undoubtedly did. That said, far fewer survived to those ages than today.