For clean, dry conditions it seems you can go quite far before wear begins to accelerate. Often more than 100 miles. I say this based on reading things over at Zero Friction Cycling, such as the chart below.
My experience has been that the noise begins to bother me before I reach the distances reflected in the Zero Friction data. It seems that once you've lost all the hot wax on the outside of the chain things get much louder. Not squeaky, as the inside is still lubricated adequately, just louder as the metal on metal sound of chain on cogs is no longer muted slightly by the chain's exterior coating.
You can quiet things down again by applying a wax drip lube, like Squirt or Silica Super Secret. Just be sure to apply after a ride, so they have time to dry.
I do find these drip on water/wax emulsions don't last long at all in the slightest bit of moisture. It's usually very, very dry where I live, but we had an extremely wet winter leading to a lot of water crossings on my MTB rides. It seems to only takes one or two stream crossings to totally remove the drip wax. Shifting was still okay usually, just loud running.
In the end I tend to re-dip my chains after 5 or 6 drip lube applications. It's hard to say how much mileage that ends up being.