Even a small object like this might push or drag asteroids.out of the belt, I think.
If they've got a good read on the trajectory of C/2019 Q4, then I don't think it will have the mass to cause any issue at all, unless it strikes some other object as it passes through the asteroid belt, because the curvature of the trajectory indicates its mass doesn't appear to be that great.
My concern is the fact that we've recently witnessed two such interstellar objects transiting our solar system in a very short time frame, objects never recorded before now. Unless improvements in observation are the reason, something may have changed in our corner of space. It may be getting more crowed.
I think if we find a third one, this new phenomenon is going to get everyone's attention.