Reaction of ethene with ammonia and sodium
No, because for ethene, $\mathrm{p}K_\text{a} = 44$. You won't be able to abstract even one proton.

Maybe, you were thinking in ethyne ($\ce{HC#CH})$? In that case, you are right! The bis-alkylation would work with sodium amide as a base! 

But is the simultaneous abstraction of both protons the most plausible reaction then?