No, he doesn't. The Tokyo Revengers manga doesn't have Takemichi's death. Instead, he plays a crucial role in the unfolding events and continues to be an important part of the story.
Takemichi's time - leaping ability in the Tokyo Revengers real story is quite unique. It doesn't seem to follow a set pattern like in some other time - travel stories. As I said before, emotions play a big role. But also, it's not something he can fully control. Sometimes it happens unexpectedly. For example, when he's in a dangerous situation and his mind is focused on going back to change things, he is suddenly transported back. This ability is what drives the whole plot as he uses it to try and make a better future for his friends and Hinata by changing the past.