You can't import animations and make them a part of the menu, no.
But there are a couple of workarounds:
1. Use After Effects, like you've mentioned. You can also use Premiere, or any application that allows you to create a movie file. Because that's what you'll be creating- a movie file which is the background of your menu.
2. Import your animated button as a DVD-legal AVI, QT, or MPEG. Make a timeline out of it. Link to the timeline from your menu using an animated video button. Then customize the button routing on the menu so the user can never actually get to that button with the remote. (You won't be able to stop them from clicking on it with a mouse, though.)