Yes its possible to do a animated boolean in maya*. Everything** you can do in maya can be animated, maya does not have separate functions for things, all things you end up doing are nodes and can be animated (maya does not have a boolean function just a boolean node). Everything you do in modeling can be animated.
example form 2006 (it was a demonstration on mesh that supposedly wouldn't boolean)
When you apply a boolean maya hides the original meshes by default, but you can still select them and unhide for easier picking. If you move the originals then you boolean regenerates too.
Mayas a bit picky on booleans with imported objects, as its dependent on poly ordering. So if the thing you boolean doesn't work detach a face then attach everything else to the face then merge points. This causes maya to reevaluate poly ordering thus fixing the mesh. As always to boolean you must ensure that the object is, at least locally manifold.
*in fact it can be animated in many different ways, it depends on if you need motionblur or not. You can achieve motion blur with shader level booleans in mentalray and prman.
** or at least as long as the tool is based on node, all factory modifications are. Its certainly possible for a user to make a function that can not be animated.
PS: this is english speaking forum, but yeah google translate works as long as you don't translate this back to German. As you already start to loose too much data.