No. When using public IP addresses, all communication between instances and services hosted in AWS use AWS's private network. Packets that originate from the AWS network with a destination on the AWS network stay on the AWS global network, except traffic to or from AWS China Regions.
In addition, all data flowing across the AWS global network that interconnects our data centers and Regions is automatically encrypted at the physical layer before it leaves our secured facilities. Additional encryption layers exist as well; for example, all VPC cross-region peering traffic, and customer or service-to-service Transport Layer Security (TLS) connections.