Nakamura improved that way.
But of course, he did more than just play blitz and bullet for 10 hours a day.
Playing tons of chess will indeed help to improve, but only if you combine that play with objective assessments of your play, and targetted instruction. There has to be a balance between play and study.
BUT, if a person is playing 3 hours of blitz every day, that person will improve much more quickly than someone who studies 3 hours of chess a week.
If someone recommends playing 3 hours of speed chess as a way to improve...
I won't trust everything they say.