Yes, it's possible.
Note that you simply will use the internal Load balancing (ILB) for GKE that makes a private LoadBalancer Ingress ip within the cluster for receiving traffic inside a similar VPC region.
In addition, since you need to configure it using path-based routing, take into account the following:
It must be an Ingress, not a Service.
Install an NGINX/Traefik IngressController.
Expose it with an ILB Service.
Add Ingresses whose annotations solely specify they must produce an NGINX/Traefik Ingress entry.