We don't have many people report it to us, but it can happen,
We believe the issue is caused by the fact that natural deodorants create an alkaline environment under your armpit, and the alkalinity causes discolouration. This seems to be more pronounced when using formulas that contain bicarb soda.
Even though we do lower the pH our Deodorant is still alkaline overall. We also use a combination of 4 different deodorant ingredients so we can use less Bicarb.
This makes the chance of darkening a lot less but it is still possible.
If you are concerned you could try a magnesium-based deodorant like Mellow or Tango - it will still have an alkaline pH but we haven't heard of them darkening the skin.