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Only in certain situations. Do you understand when it's the case?
Any real integrator has a limit. It should be also implemented in a digital controller, saturation rather than wrap around.
There are different methods to implement anti-windup in digital controllers.
Generally speaking, you'll want to stop integrator action when the manipulated values is reaching the actual limit defined by the actor. Special PID topologies like "velocity algorithm" are offering an easy way to achieve this. https://en.wikipedia.org/wiki/PID_controller#Discrete_implementation
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