No, Jo Calderone is just Gaga's alter ego. She said they were dating because it goes along with the meaning of her new single Yoü and I and the video for it. It's about loving every part of yourself, which is why she has that alter ego.
Jo Calderone was named off a few things. Gaga loves the name Joanne, which is also her middle name, so Jo is short for that. Also, her fathers name is Joe. Calderone is her grandmothers middle name. :)
Little Monster :)