You could, but only if you configured 4 of those buttons to be movement based. Think: WASD.
Or you could have just one of the buttons be a modifier that changes the stick from movement to aiming, it would be tedious, and not very functional.
Either way, to have the game be playable, you would not be able to play without movement being separate from aiming. So for decent gameplay, the answer is no. You would have to forgo a lot. Item Menus, pause screen navigation, not to mention the gameplay stuff.