Can a tankless water heater have recirculation?

Absolutely. Some units come with the recirculation pump installed inside of the unit, and they can also be adapted to pumps outside the unit. Unlike the old way of doing recirculation, the pumps will not operate continuously. They will either be connected to a timer or they have Smart learning technology that learns your hot water usage patterns, and matches the recirculation to provide hot water when you typically need it.