Not really (that I know of) because the extrude command is used in component mode whereas animation is generally done in object mode.

One way to get the effect you want is to create a blend shape relationship. Take your original cube, duplicate it, and extrude away. Once you have the desired extrusion, select the extruded cube first and THEN the original. Go ti Animation>deform>create blend shape and you'll see the original cube morph.

Hope that helps!