Apologies for the slow reply -- yes, the container has a full install of CESM, capable of running any supported compset... but limited by your memory (and, for speed, by your processors). So, for example, running a 2-degree FW2000climo will take ~27GB of RAM, and get maybe 1/10th of a SYPD or less on a typical laptop. On a workstation with enough memory and more processors, it'll be faster. (I don't think the FW2000climo @ f45 resolution works out of the box.)
What resolution are you targeting? And what kind of hardware do you have to run it on?