A bass guitarist is an important part of any band, as it creates a full sound to the song. Bass is not always noticeable when a song is playing, but take out the bass and you'll see the big difference. Bass isn't all about playing root notes, the fills often played by bass creates a stronger and smoother sound. It produces more emphasis and structure to the song.
Indeed bass is a very important part of almost any band. But there are many other ways to provide that same deep, resonating effect without a bass guitar (which I assume is what you mean by "Bass"). You could use a traditional bass, a tuba, a bass clarinet, or a whole host of other instruments to provide that stronger, smoother effect.