What was the purpose of the guitarist on the chase?

The purpose is to play the historic role of the drummer boy:

Until well into the 19th century, western armies recruited young boys to act as drummers. The drums were an important part of the battlefield communications system, with various drum rolls used to signal different commands from officers to troops.

In fact, you're not the only one wondering why this guy's in the film. Alex Zalben of MTV News asked the question of Colin Gibson, the film's production designer... oh, and as an added note, it actually works!:

MTV News: There’s a lot of crazy elements in the movie, but every time that guitar guy appears you can’t take your eyes off of him… So where did the initial genesis of that look and of that idea come from?

Colin Gibson:

Well, the initial genesis I have to say, when I came in — when I was offered the project — there wasn’t a script, but there were all the storyboards. And every armada, every battle, every army, has a little drummer boy. Uncle George, being George Miller, imagined the biggest little drummer boy in the world.

So the plan basically was to try to come up with a vehicle, an idea that could be heard over the roar of a couple of hundred amps. And the only way to do that was to build the largest, last Marshall stack at the end of the universe.

Bungee cord included, the best guitarist in the world in front of it — and then backing with some tiger drummers and basically trying to build the drums more and more. We ended up with an 8-wheel drive, an ex-military rocket launching track to give us enough scale, and then turned the reverberators and built them out of old air conditioning duct steel.

With that and a little stage and a huge PA system — and then George cast a fantastic singer performer, cabaret artist called iOTA in the role of Coma the Doof warrior. And the Doof machine basically was just that. It was a huge thing that went “Doof, doof, doof,” and gave us the beat of the battle.

And as to the character's backstory:

MTV: George also came up with this incredible back-story for everyone… I imagine the Doof warrior has a backstory, too?

Gibson: Pretty much everybody had to have a reason for existing. His reason for existing was that he could play the guitar — and there was sort of a theory of what the social hierarchy and everything was: you were either available to do battle, as a war boy; or you had a higher status than anyone else; or you had a particular skill.

Obviously mechanical was the strongest of those [skills], but this was one, too. And though he was born blind, and ordinarily that would of meant you had nothing, and [they would] break his legs and leave him on the hill, Spartan style. But he had this talent to play the guitar — so he certainly had earned his place in the pantheon.

There's a ton more info in the article, so I strongly recommend you check it out.

There were also drummers (I believe there were four of them, playing bass drums).

A couple of possibilities: As motivation the warboys. The drummers played a driving beat, and the guitarist/bassist accompanied that beat with swelling riffs that would keep the war party pumped up.

It was entertaining to the war party. This coincides with motivation, but the warriors were not pursuing their own interests, but the interests of Immortan Joe. (It could be said that pursuing his interests was an indirect way to pursue their own, but they really were more like dogs, hoping to make their master happy and didn't have much personal agency). Adding a little entertainment to their day was a small thing that could keep them on task.

It frightened any one they were pursuing. It's hard to sneak up on anyone with several 2000 horsepower war rigs riding in convoy. But throw a guitarist with a wall of speakers playing loudly, and your enemies will know you are coming. The fact that you don't need to sneak, and proclaim your presence loudly, is a sign of confidence, and probably of superior military might.

Immortan Joe liked it. This seems the most likely, since Immortan Joe got everything he wanted and the entire population of the Citadel catered to his desires. So I would venture that he liked having a psycho guitarist riffing while he drove his war rig.

Also, it is a nice tip of the hat to the warrior of the wasteland, Lord Humungus, the ayatollah of rock-and-rollah.