The boolean operation is visible only in Object mode. As usual, with a modifier, you must activate the display if you want to see more than the original shape in Edit mode… Well, except that the Boolean modifier has no option to see the modified mesh in Edit mode.
Any way, it wouldn’t be much useful to see the mesh resulting from a boolean with a dynamic animation. There’s nothing for you to edit. The Default cube is all you need to unwrap… altho I wouldn’t even bother and use a pure procedural material in Cycles, like glass with absorption.
If you really insist on seeing the modified mesh, apply the Boolean modifier… Of course, you’ll lose the animation in the process.