Genuinely don't know and don't like 911 since police are involved.
911 dispatcher in the US here
This will vary a lot from one jurisdiction to another, I can really only speak to county I work in
But while in theory every EMS call also gets a police response, probably more than half of them the only action the police take is to tell us "not responding unless requested"
And if they do respond, a lot of time they don't do much besides sit at the end of the driveway with their lights flashing so the ambulance can find the house easier.
Things like overdoses, assaults, shootings/stabbings, psych emergencies, cardiac arrests, etc. they do of course show up to because they may actually need to do something.
And if you live in a bigger city or rougher part of the suburbs, sometimes they may even take their sweet-ass time getting to those.
And if you live in a rural area, there's a decent chance you're covered by some part time or regional police department, or state police/county sheriffs who are stretched way too thin covering a huge area with maybe 2 or 3 officers on duty at any one time, they're probably not gonna show up in a hurry if at all either.
Like I said, it varies a lot, some towns in my county I can count on police being there before the ambulance (whether or not they actually do anything once they're there in a different story) and in others the cops don't give half a fuck unless someone is actively dying.
If you do find yourself calling 911 though, for the love of God, don't tell them you don't want police on your medical call, I swear that might be the most surefire way to make sure they do actually show up in a hurry. If that ends up in the notes of the call it makes the cops think you're hiding something or I don't know, planning to jump the EMS squad or something, some cops can be pretty panicky, paranoid weirdos like that, or sometimes just spiteful.