Pokémon Go Plus while driving

You will be able to capture Pokemon while driving with the Pokemon Go Plus accessory.

From here:

Capturing using the PoGo+ was a complete mixed bag, at home capturing the mons that spawn around my house I captured 5 out of 24, whilst driving I captured 10 out of 12.

Here is another:

Sooo I never play while driving, but with the Plus on my steering wheel, i can keep my thumb on the button.

In 30 minutes, I caught 25 pokemon, and 15 got away.

Also, this link alludes to encountering Pokémon while driving:

And if you’re wearing the Plus band while driving or riding in a car or bus, the Plus band might feel like it never stops buzzing. It’s a much safer option than trying to play on your phone while driving, but the vibrations can be overwhelming if you’re driving through a populous area.

Adding a new answer to add some info that wasn't covered in the existing answer.

The speed limit for Pokemon Go is 20mph. For Pokemon Go Plus it's 30 mph. This is obviously superior for egg and buddy distance.

At normal driving speed, you'll still be going too fast for Pokemon Go Plus to function. But when you slow down for various reasons, such as slowing down in traffic or a slower road, the Go Plus will start working again faster than normal Go. This also means it starts working for a longer period if you have to come to a stop (starts working earlier and later when you return to normal speed).

Go Plus also "catches" Pokemon faster than normal Go. The beeps are faster than manually clicking on a Pokemon, waiting for the animations to close, and then closing the captured Pokemon screen. So you can attempt to catch Pokemon faster with Go Plus than with normal Go. The normal Go Plus downsides of only have 1 attempt with Go Plus, only using Pokeballs, and only using normal unboosted throws apply though, so whilst you may have more catch attempts, you may have a lower success rate and ultimately catch less Pokemon than if you were a passenger playing normal Go.

Note that with Pokestops, Pokemon Go Plus takes longer to load the Pokestop than with normal Go. Go Plus has to finish a series of beeps before you can actually spin it (this was possible before, but not now, you used to be able to interrupt these beeps). A common scenario whilst in a vehicle is that Go Plus detects a Pokestop, but by the time you can spin it, it's already passed by and you're out of range. Due to this, often you can only spin it when you slow to a complete stop. With normal Go, you can load the Pokestop earlier and thus spin it earlier whilst you're still in range (pending the lower speed limit for actually getting items). Go Plus will also prioritse catching over spinning. If you sole goal is to spin Pokespots, you may be better off using normal Go.

And of course you can never attack gyms / raids / trade / battle other players with Go Plus - normal Go will always do that better whilst in a vehicle.

FYI I'm assuming you're a passenger instead of driving playing Pokemon Go.