My opinion on this has always been that it didn't change Sega's fate. Sure, I'm sure there were some lost sales. But other media formats that were easily duplicated, like cassettes and even CDs at the time, were successful and the easily pirated nature of the media didn't kill it. What killed CD sales was the convenience of digital distribution, not the fact that the music was distributed digitally illegally at first. I think even without piracy, the Dreamcast would have sill been overshadowed by newer hardware. Not just PS2, but Xbox and Gamecube. There simply isn't room for 4 players in the market fighting for the same space. And we've seen that 2 might actually be the best, with a third player going their own way.
Even if the software was easily pirated, you still had to buy a Dreamcast to play those games. If everyone was just pirating games, why didn't the hardware sell better?