Nope. There's some pretty awsome accapella groups like the Big Bing Theory. No bass.
But even if you're not accapella I've heard some decent songs without bass. I think you'll be fine without one.
Tim Gaines is the original bassist from the 80's incarnation of the band .When they reformed in 2005,the new bassist was Tracy Ferrie but now Gaines is back...so Tim is the bassist once again.