The chances that you would be able to start SSH or Telnet session from an EEM applet were pretty slim, but the comment from melwong triggered my curiosity and I simply had to try it. After all, as the action cli command uses a VTY line (like a regular user session), you might be able to use the pattern option of the action cli command to write something similar to an expect script. This was my best shot at getting it done:
event manager applet SSH
action 0.9 cli command "enable"
action 1.0 cli command "ssh -l ssUser R2" pattern "word:"
action 1.1 cli command "ssPassword" pattern "#"
action 2.0 cli command "clear ip route *" pattern "#"
action 3.0 cli command "exit" pattern "#"
My applet got past the SSH authentication (debugging on R2 confirmed that the SSH session was started) but could not send data through the session itself (it hung on the clear ip route command).