No, the anxiety people felt when they shelled out their hard earned cash on one of Sega's rather expensive machines predates the Saturn. Remember, in 1996, they were releasing games on something like six consoles - MegaDrive, Saturn, Master System, Game Gear, Mega-CD, 32X and Pico. Sega never managed to focus during that time, so a lot of the systems never lived up to their potential. Hell, they also had the Neptune being hashed out, and within a year they began working on Eclipse and two separate 128 bit projects.
At the end of 1996, Sega dropped support for everything but Saturn. They let a number of quality Genesis games go unadvertised. They killed the 32X, roughly a year and a half after it was released. Consumers were pissed. So we're third parties.
Next year, in 1997, the company said the Saturn was not the future of Sega. It took two years. Two. Understandably, the system sold horribly in 1997, and barely at all in 98. How many games did Sega put out on Saturn in 98? 3-5?
If Sega had focused on the Saturn, never spent money on the 32X, or Neptune, or Eclipse or any of that, the system would have done fine. Sega could have rebounded from a disastrous launch by 97, and all the money they could have saved would have gone in to games. Moreover, many of the games released early in the Dreamcast's life cycle would have gone to Saturn, and since many of them started on Saturn anyway, they could have been completed cheaper and more quickly than they originally were. Bringing back things like the Sega Scream would have helped to. It seems like the company could have done just fine sticking with Saturn for two or three more years, and probably could have probably fixed their image problem in time for a Dreamcast in 2000 or 2001.