I'm not talking about CAIS in particular, no.
There are many DSDs.
Very rarely, someone can be XX (or X) in some parts of the body and XY in other parts. Obviously, I'm not talking about fully functioning male and female anatomy occuring side by side, but there can be vestigal/atrophied/partially functioning organs of both sexes present in one human body on very rare occasions. Menstruation has been reported in the scientific literature in at least one of these instances to my knowledge.
People with CAIS usually don't have internal female anatomy, but in some extremely rare cases it is possible to have some degree of ovary/uterus/fallopian tube like structures with CAIS. I don't think menstruation has ever been reported in this situation.