In the film, can Hank Pym/Ant-Man only control ants who have been outfitted with his receivers?

No, I believe the device Hank Pym invented can control ants anywhere.

We see Scott controlling what appears to be thousands of ants, including ones that he seems to summon at random (e.g. in Hope's car), and don't appear to have anything special done to them.

I'm not entirely sure what the devices that the ants are fitted with are supposed to be, but Hank's explanation for how his device works implies that it releases pheromones that the ants naturally want to respond to. The things hooked up to the ants are likely other random things (like cameras, bombs, etc.)

Some of the ants are outfitted with various pieces of equipment, but that's just to make them more useful to the Ant-Mans.

The transmitter controls the ants by converting the wearer's thoughts into electromagnetic pulses that the ants then process like they would pheromones. So he uses some form of electromagnetic radiation to fake out the ant's pheromone processing ability, which in turn lets him give them orders. He can do this to any ants, nearby or far away.

No, the ants are not fitted with receivers, the transmitter/receiver that is built into the helmet and earpiece talks directly to the ants' antennas. Hanks gives the "sciencey" explanation in the film:

Hank Pym: I use electromagnetic waves to stimulate their olfactory nerve center. I speak to them. I can go anywhere, hear anything, and see everything.

_Ant-Man

Then in Marvel's Ant-Man: The Art of the Movie we get a little bit more detail of how it works.

The ants are controlled via a small earpiece in the Ant-Man helmet. To help Scott learn to communicate with the ants, Hank gives him the earpiece to practice. The device functions much like the ant's antennas: It conveys information from the user, sharing thoughts and demands with the ants. The ants will only comply when the user is clear and focused--not Scott's strong points.

_{Marvel's Ant-Man: The Art of the Movie}

The devices we see fitted to the ants are actually things to help utilise them better. For example we see the following:

• Cameras

  

• Saddles

  

• Electric shock devices (these are what we see Hank make and shrink and Scott attach I believe)

  

We also see the winch ant that lowers Scott in to grab the Yellowjacket suit and a few others. In Marvel's Ant-Man: The Art of the Movie we also have a bunch of concept art for even crazier ideas the ants could have had attached for them but were abandoned.