Choke Cherry Tree has no cherries, is this normal?

I don't think yours is a choke cherry if it has pink blossoms. Choke Cherries have white blossoms. They also tend to have multiple trunks. Could it be that yours is a crabapple or cherry? Crabapples have a similar leaf. In that case you would have to have a second tree for pollination to make fruit. If you are not going to do anything with the fruit just enjoy your tree and forgo the cleanup needed from dropped fruit and the spraying to get the bugs that prey on the fruit.