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, I wish we could say there is no chance.
If you are concerned you could try a magnesium based deodorant like Woohoo Mellow or Tango - it will still have an alkaline pH but we haven't heard of them darkening the skin.