You are assuming that the Ancient Greeks believed that their Gods were humanly visible, which is unlikely. Therefore, whether or not they climbed Mount Olympus, the Ancient Greeks would not have expected to visibly see their Gods.
From Classical Myths by Barry B. Powell (a textbook often used in undergrad classics courses):
In other myths, the setting is an obscure place: the underworld, which no one in the real world ever visited; Mount Olympus, which really exists but in myth is the home of the gods; or Crete of a very long time ago.
The events of divine myth usually take place in a world before or outside the present order where time and space often have different meanings from those familiar to human beings.
Basically, their Gods were there, but not humanly visible. That makes sense.
As to whether or not the Ancient Greeks ever climbed Mount Olympus, some sources say that they did and left offerings there for their Gods, later discovered via archaeological excavation.
The first men to reach the summit (as far as we know) were Frédéric Boissonnas and Daniel Baud-Bovy in 1913. But from the peak Aghios Antonios you get a view of the two highest peaks.