[intended]

The answer is yes

After the change in 2016, aadhar no longer gives only a confirmation/negation, it also provides demographic information aka full name, and address + a few more features.

Surnames are highly distinctive especially when combined with address data, so yes Aadhar now will provide you with enough information to assess caste.

Furthermore - since when do mobs and angry people worry about 100% accuracy. In the throes of emotion, close enough is good enough.