They can sponsor spouses, but there is a wait for a visa number of about 2 years. During that time, the spouse may only be in the US with a valid status like that of a guest worker or student (needed to be on that status before filing)..
A citizen can file for spouses as an "immediate relative" for which the wait on a visa is shorter. The fiance visa option is also available but has a number of requirements.
However, the returning resident criteria is supposed to be very difficult to meet. A GC holder who just chose to remain outside the country - even to be with family - is unlikely to qualify.

