Can a governmental entity who also has a 501©(3) exemption establish a 401(k) plan?

Yes, if the governmental employer could do it whether or not it had 501©(3) status. Layering on the 501© (3) status can get you a 403(B) plan, but not a 401(k) plan.

Just to clarify, a state or local governmental entity cannot establish a 401(k) plan if it doesn't already have one. (Figuring out whether it already has one can be difficult, since the definition of employer in a governmental context is often unclear, but this is the general rule.) This rule is not affected by whether the state or local governmental entity is also a 501©(3).