AWS | Gitlab Runner Session Stickyness

I am trying to setup GitLab in HA on AWS, I would want the Runners to run as part of different VPC. Also I would not prefer to have VPC Peering between the GitLab Web VPC and the Runner, and I intend to leverage AWS Private Links for the connectivity from Runner to Web.

And since its always the Runner who initiates communication to the Web and never otherway round, AWS Private Links ( VPC Endpoints ) is a good choice, unfortunately, AWS only allows Network Load Balancer to power the VPC Endpoint, since NLB are TCP Level, I cannot have session stickiness, to one of the GitLab Web Hosts running behind Load balancer.

Q : Does the Runner require session stickiness to function ?