Time complexity O(m+n) Vs O(n)
Yes:
$n+m \le n+n=2n$ which is $O(n)$, and thus $O(n+m)=O(n)$

For clarity, this is true only under the assumption that $m\le n$. Without this assumption, $O(n)$ and $O(n+m)$ are two different things - so it would be important to write $O(n+m)$ instead of $O(n)$.