If I move a User to a different Sub-Account will it affect their Completion status?

Once a User has completed a module that status will remain that way until you Reset Training for them.  The "Completed" status for each module will stay in their training record for the year.

However, a User may change to an overall "Incomplete" status if they had previously completed all training and are then moved to a different Sub-Account that has additional Mandatory modules in its training policy.