Yeah that will work but again, the RX 4.1 is designed for short-pull road brakes, the 5.0 is compatible with v-brakes.
But if you're going to use your current levers and mount them on the underside (what I'm probably going to do), you cant use that handlebar because the clamp diameter (not the center, the rest of it) is 23.8mm and all mountain bike hardware is all 22.2mm