Is there an ssh server for Android (such as openssh for Ubuntu) that will allow me to access my device console via PuTTY?
Yes, there are a couple of options for this, including:
Some of these apps will require you to root your device. SSHDroid, QuickSSHD and SSHelper, at least, do not (there may be others as well). There are certainly multiple choices for you to investigate depending on your requirements/desired features/etc.
You can also use an SSH server without a frontend app -- starting it with a command or through a configuration file, as described in Howto: Connect to Device with SSH.
According to that page, CyanogenMod included an SSH server (dropbear) in some releases. ("Cyanogenmod 9.0 RC2 no longer includes Dropbear.") Or you could probably put it into your system yourself.
It seems that by default it is assumed that the server is run by root (i.e., you'd need root acces to your system), but it must be possible to set up it to work without root.