Suppose I am setting up a new name server at ns1.example.com, and I have properly created the glue record at my registrar to tell the registry that ns1.example.com should point to my name server's IP address at 77.77.77.77. Is there anything in the configuration of my name server that needs to also publish this IP address in a zone? I.e. publish an NS or A record for itself?
If the name server didn't publish its own IP address (aside from in the registry glue record) would clients still be able to query me for other records successfully?
The name server needs to publish its own record for the name. Glue records should only be used to "bootstrap" discovery, and then be discarded in favour of the result retrieved from the actual authoritative nameservers. I'm not entirely sure what recursive resolvers will do when they get
NXDOMAIN
for a record they got glue for, but I'm pretty confident it won't be pretty, nor consistent between implementations.