No, BioShock 2 does not have a traditional New Game+ mode (carrying over weapons, plasmids, tonic slots, research, and Adam from a completed save).
2K Marin designed the single-player as a self-contained narrative arc. The power curve (fully upgraded drill, max plasmids) would trivialize the early game's horror/resource scarcity. The DLC Minerva's Den is often cited as the "better campaign" and is standalone.