Is it possible to set a timeout on openssl's s_client command?
Use timeout command from GNU coreutils package.
timeout <time> <command>
Alternatively look at the first response to this archived blog post for a bash-only answer.
for the first loop: while read servername;do
timeout 2 bash -c "/dev/tcp/$servername/$Port" && echo Port open. || echo Port closed.
done
But the open ports is more dificult: timeout 1 openssl s_client -showcerts -connect $servername:$Port