As far as I'm aware, yeah, you're still invulnerable. It still requires the timing to pull of the multi-jump as well.

As for why they combined them, it would be pointless to include the Screw Attack into a Metroid Prime game without the multi-jump attached to it. Doing so would create a gameplay mechanic in which the view would pull out into a 3rd-person perspective every time Samus jumps, as opposed to just pulling the view out for when she activates the multi-jump. It would be too disorienting.