Can an ECS Without an EIP Bound Access the Internet?

Yes.

You can use the NAT Gateway service to allow ECSs in a VPC to access the Internet using an EIP. The SNAT function provided by the NAT Gateway service allows the ECSs in a VPC to access the Internet without requiring an EIP. Additionally, SNAT supports a large number of concurrent connections for applications that have a large number of requests and connections. For more information about NAT Gateway, see NAT Gateway Service Overview.

You can configure the SNAT server so that the ECS without an EIP bound can access the Internet.

For details, see "Configuring an SNAT Server" in Virtual Private Cloud User Guide.