No, not unless there is a Z clause that specifically requires this.
The unamended ECC defines a Subcontractor as someone who has a contract with the Contractor. A Subsubcontractor in an ECS does not have a contract with the Contractor in the ECC, the subsubcontract is between the Subcontractor and the Subsubcontractor.
The unamended ECC defines a Subcontractor as someone who has a contract with the Contractor. A Subsubcontractor in an ECS does not have a contract with the Contractor in the ECC, the subsubcontract is between the Subcontractor and the Subsubcontractor.