Well, look at it this way - WCW lost $15 million in 1999 and $62 million in 2000. That's $77 million in just two years. A pretty disastrous loss of income for any company. And this is when Ted Turner was still funding them. As soon as Bischoff bought the company from AOL Time Warner, the only way they would have stayed in business would have been like Vince McMahon and WWF/E, having to rely on the income they make from live gate/PPV/merchandise/licensing/etc., rather than some multi-millionaire/billionaire who owned the company.
On top of that, the main reason WWF/E became a publicly traded company was because of Turner. By becoming corporate, they allowed themselves to avoid any situation like when they were a private company battling the massive funds that Ted Turner had for WCW. Without that advantage dead set against WWE anymore (the shoe would have been on the other foot completely here lol), would Bischoff have stood a chance? WWE was not only adding fresh blood to their roster (Cena/Lesnar/Batista/Orton/Shelton/Haas/Rico/etc.) but they could have used the funds they had to buy out any WCW talent they wanted.
So yeah, unless Bischoff and company got their shit together and got their heads screwed on tight, then they wouldn't have stood a chance. Looking at all the evidence, they likely wouldn't have anyway. They almost certainly still would have gone under.
