Training on derived features that won't be present in a test set
Thats not how it works, there is not juice to be extracted if the data is missing from the test set.

You will have features in train that might be discriminative, but missing in test. Then when you try to predict there wont be any inputs that you can map to the outputs.

This beeing said I should mention that NaiveBayesclassifier will not use missing features, so there would be no harm in including them but you wont get any additional information, just more unnecessary complexity.