Maybe it will keep Gro$oft out of consoles market *at all*. Or I am confusing dates a bit - when came out X-Box, the planing in fact?
IIRC, the plans for a Microsoft console began in all the way back in 1998. Bill Gates finally became convinced that a console was viable and gave the go ahead. It just so happened that Sega and Microsoft became close during the Dreamcast's brief lifespan (in fact, Microsoft was one of the potential buyers when Sega went belly up c. 2001/2002, actually). In a scenario where the Dreamcast somehow keeps Sega in, I don't see how long they can last. The Atari era proved that a market saturated with many consoles is untenable. The weakest link will sooner or later bite the dust, which sadly happens to be Sega.
As for outselling the PS2...I don't think it's possible, to be honest. One of the big selling points for the PS2 was its DVD capabilities. Unless Sega can wise up to including one earlier, which there were actually plans to eventually release an add on that would in OTL, it'd remove a lot of the earlier draw of Sony's PlayStation successor. Not to mention, bootlegging games was also what really, really hurt Sega. GD-ROMs were very easy to rip from. Loss of sales is something that Sega desperately needed to avoid at this point. Ultimately, though, Microsoft and Sony have the muscle to shrug off setbacks (especially Sony); Sega, however, does not.