Does it make sense to get to Fenghuang Ancient Town from SHENZHEN by train? If yes - How?

There is no direct train between them. You can take high speed train from Shenzhen North Railway station to Changsha South Railway station, and take metro line 2 to Changsha train station. Around the train station, there are many buses go to Fenghuang ancient town directly.

Thanks. That's exactly what I did!