Can an auto insurance policy be cancelled if the insurance company deposited payment in full?

Yes they can. But they will have to refund any unearned premium to you. Each state has it's own regulations that determine how and when the Insurance Company can cancel a policy and most companies stricltly adhere to the regulations. IE, Fraud or Misreprentation on the Insurance Application. Claims within the first 60 days of a policy, Undisclosed drivers, Undisclosed accidents or tickets, Failure to fully disclose a risk, etc.