Is the proper pushforward of a degree $d$ branched cover $Y \to X$ equal to $d[X]$?

Question

Consider a branched covering $\pi:Y\to X$. If we restrict to the unramified locus $\pi_{un}:Y_{un} \to X_{un}$ then the proper pushforward of $[Y_{un}]$ is exactly what I expect it to be, $d[X_{un}]$. In addition, if I restrict to the ramification locus, the degrees of each ramification cycle (in the source) should add up to $d$. Does this imply that the ramification locus is what I expect it to be?