Some fraction of it, yeah for sure, how much of it exactly is debatable. I think at the angle she is holding it at it doesn't seem too bad at all. Whatever minimal force exerted on her at such a steep angle is mostly directed "down" (she would feel it as though she was being pushed into her seat) with only an even smaller fraction of that applied as torque to flip her back.
What she's using in the gif is meant to stand in for an AT4 or something similar, which is a recoilless weapon. What's shown in that youtube clip is a missile launcher. The recoilless aspect of the weapons overlap a little, but the thrust from a missile comes from its rocket motor, while the thrust from the AT4 comes from the propellant.
Here is an old simple demonstration of an early (from ww2) recoilless rifle which is more comparable to the weapon in the anime than what's shown in that other youtube clip. It compares the recoil to that of a regular firearm and i think it's quite informative.
https://youtu.be/qsM8EtBZ-EQ?t=62