No, we do not have Object "layers" in A:M in the sense that Maya does.
We do have "selection filters" which can identify and display any subset of bones (or any other keyframeable thing) in a model. This is a functionality very similar to "selection sets" in other software.
Enhanced Selection Filters, further explained
I use them for quickly isolating just the spine bones or just the finger bones in the PWS view while I am animating.
You mentioned wanting to export only certain bones. Let's say you animated something, then baked it so it could go to a game engine, maybe? Perhaps at that point you only want to export the bones that mesh is attached to?
You could make a selection filter for all the bones you do NOT want to export and use that to call them up when you want to delete them in one swoop.
Is that anything like what you are wanting?