When cats eat flea eggs do they hatch into worms?

Yes....By swallowing a flea infected with a tapeworm larvae.

This process begins when tapeworm eggs are swallowed by flea larvae (an immature stage of the flea). Contact between flea larvae and tapeworm eggs is thought to occur most frequently in contaminated bedding or carpet.

Next, the pet chews or licks its skin as a flea bites; the flea is then swallowed. As the flea is digested within the pet's intestine, the tapeworm hatches and anchors itself to the intestinal lining.