By default, all items that normally require a shovel or a pickaxe to break are breakable by the drill. However, if you have the mod Iguana tweaks installed, that one might screw that up.
Actually Aroma The Shovel ToolClass has only the Blocks: Snow & Snow layer inside them and not the ground material (which would be nessesary here)... Its actually a bug that he can not mine dirt and grass fast xD And Multi Tool registration in 1.7.10 without special handler was bugged... as far as i can remember right...