No. Earnest money is not necessary to make an otherwise accepted offer into a valid contract. Earnest money is a buyer-performance item required to be deposited after a contract is fully executed. A contract could become effective even if no earnest money is required in the agreement.
While a seller could instruct an agent to only present offers that include an earnest-money check, an agent who decided himself that he will not present an offer without an earnest-money check may be violating the Code of Ethics’ instruction to present all offers as quickly as possible.