According to the book, no. Firemen do not also put out fires in Fahrenheit 451. Credit to @TangoOversway for remembering that this was mentioned in the book.

From a conversation between Clarisse and Montag:

They walked still further and the girl said, "Is it true that long ago firemen put fires out instead of going to start them?"

"No. Houses have always been fireproof, take my word for it."

"Strange. I heard once that a long time ago houses used to burn by accident and they needed firemen to stop the flames."

He laughed.

Later:

Montag hesitated, "What--was it always like this? The firehouse, our work? I mean, well, once upon a time...."

"Once upon a time!" Beatty said. "What kind of talk is that?"

Fool, thought Montag to himself, you'll give it away. At the last fire, a book of fairy tales, he'd glanced at a single line. "I mean," he said, "in the old days, before homes were completely fireproofed--" Suddenly it seemed a much younger voice was speaking for him. He opened his mouth and it was Clarisse McClellan saying, "Didn't firemen prevent fires rather than stoke them up and get them going?"

"That's rich!" Stoneman and Black drew forth their rule books, which also contained brief histories of the Firemen of America, and laid them out where Montag, though long familiar with them, might read:

Established, 1790, to burn English-influenced books in the Colonies. First Fireman: Benjamin Franklin.

RULE 1. Answer the alarm swiftly.

     2. Start the fire swiftly.

     3. Burn everything.

     4. Report back to firehouse immediately.

     5. Stand alert for other Alarms.

Book passages were found on Amazon.com using the Search Inside page for Fahrenheit 451.

According to the book, no. Firemen do not also put out fires in Fahrenheit 451 because houses have been fireproofed. When houses were fireproofed, firemen switched from putting out fires to burning books.

From a conversation between Clarisse and Montag:

They walked still further and the girl said, "Is it true that long ago firemen put fires out instead of going to start them?"

"No. Houses have always been fireproof, take my word for it."

"Strange. I heard once that a long time ago houses used to burn by accident and they needed firemen to stop the flames."

He laughed.

Later:

Montag hesitated, "What--was it always like this? The firehouse, our work? I mean, well, once upon a time...."

"Once upon a time!" Beatty said. "What kind of talk is that?"

Fool, thought Montag to himself, you'll give it away. At the last fire, a book of fairy tales, he'd glanced at a single line. "I mean," he said, "in the old days, before homes were completely fireproofed--" Suddenly it seemed a much younger voice was speaking for him. He opened his mouth and it was Clarisse McClellan saying, "Didn't firemen prevent fires rather than stoke them up and get them going?"

"That's rich!" Stoneman and Black drew forth their rule books, which also contained brief histories of the Firemen of America, and laid them out where Montag, though long familiar with them, might read:

Established, 1790, to burn English-influenced books in the Colonies. First Fireman: Benjamin Franklin.

RULE 1. Answer the alarm swiftly.

     2. Start the fire swiftly.

     3. Burn everything.

     4. Report back to firehouse immediately.

     5. Stand alert for other Alarms.

Later in a conversation between Beatty and Montag:

... "So! A book is a loaded gun next door. Burn it. Take the shot from the weapon. Breach man's mind. Who knows who might be the target of a well-read man? Me? I won't stomach them for a minute. And so when houses were finally fireproofed completely, all over the world (you were correct in your assumption the other night) there was no longer need of firemen for the old purposes. They were given the new job, as custodians of our peace and mind, the focus of our understandable and rightful dread of being inferior: official censors, judges, and executioners. That's you, Montag, and that's me."

Book passages were found on Amazon.com using the Search Inside page for Fahrenheit 451. Credit to @TangoOversway for remembering that this was mentioned in the book.