Hi everyone,
Let me answer myself 
It looks like the answer is yes.
I’ve finally found this documentation page…:
https://kubernetes.io/docs/concepts/services-networking/dns-pod-service/
… mentioning this note:
Because A or AAAA records are not created for Pod names, hostname is required for the Pod’s A or AAAA record to be created. A Pod with no hostname but with subdomain will only create the A or AAAA record for the headless service ( default-subdomain.my-namespace.svc.cluster-domain.example ), pointing to the Pod’s IP address. Also, Pod needs to become ready in order to have a record unless publishNotReadyAddresses=True is set on the Service.