Somewhat, at least as far as Logan's time in the first months after escaping Weapon X. The book was written by the same guy who wrote the novelization of Weapon X, so it's basically a sequel to that book. One of the early chapters, with Logan recovering from the berserker rage that had him eating the wolf in the prologue, is pretty terrific.
And there's another scene later where a new crew is trying to re-open the Weapon X facility, and during the cleanup someone finds a human head in one of the air ducts.
A lot of it gets kind of silly though. One of the failed experiments he fights is a guy that belches fire. And they added a bunch of new characters who take up so much time that Logan almost becomes a side character.
But it's a decent enough book, definitely worth a read.