Do I need an internal ELB if I already have a public ELB pointing to the same location?

Bit of an odd question about AWS + ELBs.

We have a VPC that contains public and private subnets. Within the private subnets, we have 2 applications (application 1 and application 2) deployed using ASGs, and each is reachable by it's own public ELB.

Application 1 also needs to talk to application 2, one is a website and the other is an API service. I was just wondering if I needed to setup an internal ELB for application 2 given that I already have a public ELB for it?

If it makes a difference, all the instances communicate with the outside world using a NAT. Is AWS clever enough to route the traffic internally, or will it go out and back in? If the latter, it definitely feels like I should add an internal ELB.

Cheers