You can, but you need additional components to do it, like an SSH session broker (i.e. a gateway or proxy). Some of these, like SSH Communications' PrivX suite,

You can, but you need additional components to do it, like an SSH session broker (i.e. a gateway or proxy). Some of these, like SSH Communications' PrivX suite, can record all traffic running through the proxy. It's not all that different from HTTPS security and auditing proxies.