the inner 2 13mm bolts in that picture will hold the engine up if you take the bumper off, you can just see them hidden behind the white plastic clip in that picture. This assumes the bolts are still there and not stripped. so you dont have to support the crossmember when removing the bumper if those 2 bolts are in place.
however if you arnt 100% sure about the condition of them, supporting crossmember is a wise precaution to take