The Wolverine grossed more than $400 million. It is one of the most popular movie franchises of this decade. The newest movie is sure to offer something for people who were fans of the first two, as well as something for new fans who have not seen the previous movies.
Whoever they get to replace Hugh Jackman will have some huge shoes to fill as he has defined the role for a generation of fans, but it is certain that Wolverine will continue to be a popular character in any incarnation and that there will continue to be moves that feature him.
Superhero movies tend to do well at the box office even when they are universally panned by critics and audiences, as we have seen this summer with the lowly rated Suicide Squad. Therefore it is likely that Wolverine's successor will prompt another huge franchise as it will attract people to the cinema even if the films are not critically acclaimed.
No, Wolverine's success is based on the performance that actor Hugh Jackman has brought since the beginning. As such, it would be highly unlikely that any successor could hold the same allure. The very image of Wolverine has become entwined with that of Jackman. Even if the successor's film(s) were enjoyable, it would be very hard to not recall and compare to the original Wolverine.