sigh. NO it does not. please stop spreading dumbass rumors. when you're talking to openssh, there is a process. if not, its just a launch daemon like any other.
You could install terminal and top. After that open terminal and enter "top", which will list the running processes and how much CPU time they consume. Maybe some process is keeping the CPU really busy...
I can confirm in fact SSH does run after you install it via Cydia. You need to get BossPrefs and under the config section ensure that SSH is checked to not start on restarts and that it is also off currently. Also leaving on Wi-Fi when your not using it will also drain your battery quick too.
Yes, ssh runs as long as the phone does not sleep (maybe even then - I don't see any way to check it). However, I just played a little and it looks like it doesn't have much impact on CPU usage:
One thing that I find interesting is that Springboard spikes to 60% when moving between spaces. Wobbling consumes around ~25%. sshd sticks to 0%, but the relevant part should be if it's running while the phone sleeps (which would be stupid, because without WLAN there's not much use for it. For the same reason I can't check what happens in sleep mode.