Yes, and recall that before Trump ran for political office he was among the Dems in NYC and NY state.
I think he registered as a Democrat in New York State because the State has historically been governed by a Democrat, except for George Pataki. Malcolm Wilson was the last Republican in that seat since 1974, when Pataki beat Mario Cuomo in 1994. I can't remember if the State Legislature was split when Pataki was Governor, or he could have had a majority in both Houses when the Capital Punishment Bill was passed and he signed in. It was overturned by the Courts. But for quite a while now, Democrats have had an almost 2-1 majority in both Houses of the State Legislature. New York State has been screwed for a long time. I know because I retired from my job with New York State in 2003.