YES !
You CAN ssh from a a nologin account (such as daemon, apache, tomcat, ect..). The only thing you have to do is:
1 - Create global known_hosts file at /etc/ssh/ssh_known_hosts
2 - Change it's permission to 644. Note: NOT 600. Other people need to read it.
4 - Put destination host key into this file.
5 - Create a RSA keypair then add id_rsa.pub to destination account (if you use password, try yourself).
==> you can use ssh to run command remotely.
I created a PHP page (run by daemon user on system) to execute command by another user at another machine, of course using SSH.