Hmm . . . given the right circumstances, I could see that being somewhat believable though. Hell, back in 1988, Atari Corp and Sega almost did join forces (Sega wanted Atari to handle marketing/distribution of the MD for North America -Mike Katz, president of Atari Corp's Entertainment division, was in favor of the idea too -of course, he ended up at Sega at the end of the next year ).Yeah, I don't seriously think SEGA and Atari would have joined forces, but it's an interesting thought experiment.
Assuming Atari Corp actually approached Sega back around 1991 (when the Jaguar was just solidifying in its early prototype stage -first silicon for Tom rev1 at the end of the year), they very well may have piqued Sega's interest in such a project (at very least in a similar manner as the SGI project supposedly did a bit later). Plus, unlike the SGI proposal (going by the little we know about it), the Jaguar would have been much lower cost and much closer to market-ready (both the primary concerns SoJ engineers had over the SGI chipset -apparently) and the Saturn project would have been in the very early stages (if even started) so there would be little investment lost by shifting priorities to the Jaguar.
The Jaguar chipset also could have fared pretty well as a high-end 2D Sega arcade board (sort of like the ST-V, but earlier and not as powerful in some areas -more flexible in others though) -remember, the Jaguar chipset was somewhat modular (particularly in terms of RAM configuration and CPU), so there could have been a considerable boost to the arcade system while still using the same ASICs as the home console. (which is what the CoJag did with its R3000 or 68EC020 and added bank of VRAM -the Jaguar's memory map supports 2 4 MB banks of DRAM and a 6 MB bank for ROM -the 3 banks share a bus, but keep page-access separate for DRAM, so one or both DRAM banks can stay in page-mode when another bank is accessed concurrently)
Come to think of it, I think this may be my new favorite scenario for the topic . . . both Sega and Atari could have been better off and the Jaguar hardware (and Flare) would have gone to much better use. (plus the potential market changes -for consumers and developers- with a relatively low-cost early 32-bit generation platform -be it cart based or a CD system still less than 1/2 the price of the 3DO -or do both CD and cart like the Saturn+Jupiter concept)
Hell, if Atari had managed to swing that back in '91 (and got generally boosted PR and investor interest from it), their situation might have stabilized a bit more, allowing their computers and the Lynx to be better managed/supported as well. (had they kept the ST line at least reasonably relevant in its niche US market and mainstream in Europe into the early 90s, then it might have been possible to roll the Jaguar chipset into the computer line as well -that would have been really interesting to see around '93/94)