It does work for me on:
$Version
(*"11.2.0 for Mac OS X x86 (64-bit) (September 11, 2017)"*)
Taking a bit time to compute though:
conv = Convolve[PDF[CauchyDistribution[0, mu1], x], PDF[CauchyDistribution[0, mu2], x], x, y];
conv // PowerExpand // FullSimplify
$$\frac{\text{mu1}+\text{mu2}}{\pi \left((\text{mu1}+\text{mu2})^2+y^2\right)}$$
