Elastic IPs for internal private services

Can someone please clarify if use an Elastic IP for load balancing/HA of internal services, does the traffic from internal clients (located on the private subnet) to the elastic IP end up being routed to the internet?

Does the internet gateway avoid that traffic from being routed outside of AWS?
No clients should access the elastic IP from outside the private subnet, at all.
All traffic must be segregated from the internet, staying completely enclosed on the private side.

Thanks.

Edited by: jlerm on Jan 26, 2019 7:22 PM

Edited by: jlerm on Jan 26, 2019 7:23 PM

Edited by: jlerm on Jan 26, 2019 7:24 PM