FWIW, I recently contacted AOL to see if there was a way to choose which folders would be visible or hidden when the left-hand panel is collapsed. I wanted this to see if I could increase my screen real estate by having only the message list and message showing but still be able to drag-and-drop a message to the Saved Mail folder.
Unfortunately, it's apparently not possible. Individual folders cannot be hidden or displayed according to user preferences, and when the panel is collapsed, you cannot drag a message to the Saved Mail sub-folder of My Folders. You must either 1) have the panel open with the Saved Mail folder visible to do the drag-and-drop, or 2) you must use the buttons and click Actions > Move To (whatever folder).
It would be nice to have an "Archive" button to move messages to Saved Mail by default with a single click. But they don't even have that.