Yes, Eurasian Collared-Doves in Florida are wild wild wild.
They breed all over Florida. There are scattered and slowly growing colonies as far north as southern Delaware, though nests may not have been actually found north of North Carolina. I believe (a) nest(s) have been found in southern Pennsylvania. Texas is rife with them; birds have been seen as far north as south(east)ern Alaska, southern Yukon, and Massachusetts.