Yes, DoorDash may know if your license is suspended at any point after the initial background check is completed. DoorDash runs updated checks on the drivers who utilize its platform, specifically for driving records and criminal records. In addition, DoorDash uses a consumer reporting agency called Checkr to complete these background checks, and Checkr can flag new offenses for anyone already in their system. So, not only is it possible, but in theory, it is probable. So long as Checkr is doing its job, your newly suspended license will likely get flagged, and DoorDash will be notified.