Yes, but the rocket is still being a rocket, and after it leaves the tube, it'll still toss a ton of exhaust at the bike. I know it's designed to be fired stationary, but this discussion is about the feature allowing it to be fired in motion in emergencies, which hopefully nobody ever did.
And even things like the RPG-7 use a recoilless design to launch the projectile before the rocket ignites and you don’t see the user being impacted much at all by the rocket exhaust.
Err, yeah that comes out of the back of the recoilless rifle so only an issue for the people behind you not the person firing it unless they are too close to a wall or similar. With something like the RPG-7 the backblast is from the recoilless stage not the rocket.