In general, the only supported calendar in the CESM time manager is the 365 day or no-leap calendar. This calendar has the standard 12 months, but it has 365 days every year and 28 days in every February. Monthly averages in CESM are truly computed over varying number of days depending on the month of the year.
A gregorian calendar is available if the ESMF time manager is used. To use the ESMF time manager, the ESMF library has to be available locally and the ESMF library has to be turned on in CESM. See using ESMF in CESM for more information about setting up CESM with the ESMF library.