I am not sure about the cluster your talking for 3 servers.
But according to my understanding for your query,
I will make one server as master for SSH key gen and share the keys to other servers, so there would be a free login to those servers.
And for executing the script , The script is placed in the NFS directory(Master) and mounted to those three servers.
Then a basic for loop script is executed in master.
Tested: I use to create users in one shot for multiple servers.