Yes. Although, since they all have the same credentials, I think what you want would be better achieved by
You need to ensure that you have set up ssh between the servers so you can login without a password. Install the
pdsh package if you don't already have it. Once installed you can do something like:
pdsh -R exec -w ^hosts.txt screen -D -R
Please note I don't now the actual screen command you want to use. However you can execute any command,script or list of commands in parallel. The above will execute at the same time, to a list of hosts defined in the host.txt file.
pdsh is a great tool for managing groups of servers, where you need to issue commands in parallel. Look at the man page for
pdsh there are lots of options. A good one to note is
PDSH_SSH_ARGS_APPEND variable, this will let you append options from the normal ssh command.