Using kubeadm to join a GKE cluster is not currently possible (kubeadm on a node requires a token from a master that was started using kubeadm). That would be a cool use case though.

You can add an on-prem node to your GKE cluster if you manually configure the kubelet (basically what kubeadm makes nice and easy).

Your cluster may not work as expected though unless you also create a VPN connection between the on-prem node and your cloud network where the rest of your nodes are running and also configure networking routes to map a node CIDR to your on-prem node. Otherwise, cross-pod networking will not work.

In addition, features like kubectl exec and kubectl logs likely won't work for any pods running on your on-prem node.

Should be available in the near future. You should request the early access: https://cloud.google.com/gke-on-prem/