Yes, we even know that the density of such $n$ is the expected one.
A. O. Gelfond proved in 1968 ("Sur les nombres qui ont des propriétés additives et multiplicatives données", Acta Arithmetica 13, pages 259--265) that $$\lim_{N \to \infty}\frac{1}{N/a}\#\{ 1 \le n \le N: n \equiv b \bmod a, \, s_q(n) \equiv j \bmod m\}=\frac{1}{m}.$$ Here $a,q,m$ are fixed positive integers, $s_q$ is the sum of digits in base-$q$, and $\gcd(m,q-1)=1$ (otherwise there are obvious obstructions, due to the congruence $n \equiv s_q(n) \bmod {q-1}$).
Now apply this with $q=m=2$ to get your answer.