No, Liverpool don't depend on Nunez alone.
They bought him with plans to build him up as an important player of the team. Mane left. Firmino lost his form. Salah is more than 30s. So Liverpool are preparing to replace Salah by Nunez. They want to use him a main striker and get main goal resource for the club from Nunez.
But for now, Nunez is just a new player of Liverpool and he needs to contribute more, build up his role there.
The problem Liverpool is facing at the moment is the storm of injuries that hit their midfielder, the defeat to Manchester United because Liverpool always conceded in their midfield. Even though Nunez and Salah played well, they couldn't do much on the pitch because the supply of the ball from the midfield was very little. Now Liverpool must take advantage of the rest of the midfielders who are still fit, or put one of their attackers in the section to help the flow of the ball to the front line.
They got issue with injuries and I think their medical team have something wrong with lot of injuries in the past two seasons. This one is a second season they face it so it should not be coincidence.
They must check back and find what's wrong to fix if they don't want to lose their own strength and competitiveness only because of so many injuries in their team.