Stored genetics do not remove the staffing problem

Could stored eggs and sperm let a very small colony maintain enough genetic diversity?

They could preserve diversity, but without artificial gestation they would not remove the pregnancy, staffing, radiation, and care burdens on the colony.

Stored reproductive material could reduce one genetic constraint if it survived radiation. Genetic inventory still does not perform the physical work of producing and raising a new generation. Repeated pregnancies would affect health and temporarily reduce the availability of colonists who also hold essential operational roles. A technological fix for one bottleneck can move the constraint into medicine, childcare, and workforce planning.