No, because for ethene, $pK_a = 44$$\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?