Can I Call an API If the API Is Not Bound to an EIP?

You can call the API on the intranet. If the VPC in use is the one where the API resides, you can directly call the API. If the VPC in use is different from the VPC where the API resides, you can establish VPC peering connections to enable communication between the two VPCs. For details on how to create and use VPC peering connections, see VPC Peering Connection.