It's absolutely critical for your new hire's growth and development for them to complete workflows that have been assigned to them. It provides an early sense of job satisfaction and a ramp to longevity at the company. Note that you are also assigned tasks and check-in questions to support their growth and development.
When you complete and then mark your tasks as complete, the workflow moves forward and the new hire and other supporting team members are assigned further activities (tasks or check-ins). If tasks are not marked as complete then the workflow can stop at that point.
Timely completion of tasks also shows your hire how much you and the company care about them and their success. Its a stressful time for them. If they feel like they are falling behind because of lack of team support then they might become disengaged and disillusioned over time. That's a fast ramp to dissatisfaction and attrition.
Lastly if you don't mark tasks as done then the platform doesn't know that the task has been completed. In that case, the system will continue to send out reminder messages. This could clearly become annoying (especially if you actually completed the tasks). Help us not spam you by keeping the platform updated to everything you have done in support of your hire!