A bit late for the party but here goes:
No there are no conclusive studies on empaths. You can check out Judy Orloff (which xkp linked to earlier) but a fair warning; "Dr. Orloff is a psychiatrist, an empath and intuitive healer, and is on the UCLA Psychiatric Clinical Faculty. She synthesizes the pearls of traditional medicine with cutting edge knowledge of intuition, energy, and spirituality." She mentions some studies in the linked article although she fails to provide links or direct quotations from it.
I haven't seen any performance from a socalled empath that wasn't just normal cold reading. These are "psychics" under a new name IMO. Only guy I've met in real life who claimed to be an empath was diagnozed with paranoid schizophrenia which didn't help to convince me at all.
Offtopic: I have a hard time accepting there's a psychiatrist that believes she is an empath and offers "energy-based healing".