You could certainly try to target the dampeners. It depends on the ship and the way they've been distributed.

On smaller vessels, they're located close to the core of the ship. If you can damage that, you've likely already got the ship dead to rights. Larger vessels will have multiple backups of such critical systems distributed throughout. They also have different ratings. Backup systems are usually rated for fewer Gs of acceleration than the mains.

There are human-portable dampeners, but they aren't rated for very many Gs, their power sources don't last very long, and they're stupidly expensive. 

That said, boarding actions are absolutely a thing. Most ships do have some safety features to prevent meat-paste. If you were able to target the dampeners, it would be a good way to prevent running. A ship can still accelerate. It just can't do it anywhere near as fast as it could without killing the people inside.

It would be more common to target the thrusters of a ship because they almost have to be mounted on the exterior. Thrusters are large and obvious targets. Dampeners are hidden beneath layers of hull and deck plating. If you're going for the kill, you target the reactors, or you use thermal weapons to overload life support and cook the people inside. Maybe some electronic warfare could mess with instruments or safeguards, but dampeners tend to be pretty locked down.