Sorry for late answer.
I was not able to use k8s dashboard with private cluster. BTW — Google says the dashboard is deprecated (but I like to use it, anyway :) ).
About cloud build — when you deploy something on k8s you “talk” to API which is running on master host(s). Master hosts have public IP on private cluster, only workers have no public IPs. So deploying should be the same as to “normal” clusters.