it's just a div id="_busy"
So yes, you can hide or show it.
On the server side it's more complex, because you can include script in a reply, but it'll only get executed when the reply is completely formed and completely sent to the client.
so typically you unhide on the client side, and hide on the server side.
Obviously you need to full understand how the engine is using it as well, because there are other things hiding and unhiding it.
In summary - you probably should not be hiding and unhiding that graphic yourself. If you want to notify the user of things happening, use your own graphic, or a progress bar.