No why would it. They probably are already taught self defense but are cowards so will go straight for their guns because they just cant wait to use them. Shoot first ask questions later.
Yeah, that looks to be the disturbing picture being painted by each new incident that comes to light, including the most recent one where a man with his hands up in the air (surrendering) is senselessly murdered in plain daylight. But the problem is not with most police officers, the problem is that when their coworkers investigate, prosecute and sentence them,
they are not properly held accountable. There are few murderous bastards in the police force, but those that are... they're very comfortable killing when presented the slightest opportunity. Same goes with other wrongdoing and corruption.
Anyways, I dont think teaching them any martial arts makes any difference. That's because (I have heard) that the standards for the police are too low. They are in good shape when joining the force, but they're not running drills to keep in shape. They're given military surplus, but are not given military rules of engagement (which I think would be a great improvement over how they behave right now). They can be taught the deadliest martial arts, but they're not going to be expected to practice it, they're not going to be expected to hone or maintain their skills. That's what it boils down to. After a year or two, for most cops, it won't make a difference.