You'd think so, but it doesn't always work. It has to do with the pivot transform, I think. If you go down to the subobject level, and mirror the geometry, instead of mirroring the entire thing, it works. The other foolproof method is to take your main mesh, 'attach' every other subobject to it, then use the Element selector and detach the bits one at a time. That sets everything to have the same scale, rotation, and position pivots so it will import flawlessly.
I'm currently piecing together the 3DS Max tutorial on the Wikki, so you can check back there.