Does it make sense to train multiple classifiers for multiple partitions of data?
Yes, there is no need for you to manually split the dataset into two parts and train separate classifiers for them.

That's something that decision trees (eg. Random Forest), will do, as you say, under the hood.

The manipulation that you could do on your dataset is probably the dimensionality reduction - but, this is also done, informally, by decision trees. See "Random Forests / Ensemble Trees" section here.