Hello as a follower of both Amiga and Atari machines I don't think that Tramiels presence would have made things any different.
He was getting on in years even in the mid-80s, and my understanding is that he later delegated much of his responsibilities to his sons, who I believe were the main culprits responsible for Ataris downfall in the computer market.
The Jaguar could have been more successful, but it should have shipped with a CD drive, but developers were deserting Atari.
In 1994, CD was well on the way to becoming the standard media for software. Certainly this was the case by the time the Sony PlayStation shipped the following year.
Commodore at least had the CD-drive, but the hardware was too behind the curve for a "next-gen" console, marketed as a 32-bit console with graphics comparable to the more successful 16-bit Sega Mega CD, and no FMV as standard.
This was a similar scenario with the A1200, 256 colours and 2 megabytes of memory were simply not enough when it was released - even if was sold at half the price of PC's of the time.
The Falcon was a superior machine in many ways to the A1200, [I won't go into detail as that will surely spark another debate] but by this time most developers had already flocked away from Atari to develop for Amiga and PC, and later PC only, the Amiga won the war.
If it was Tramiel in charge and we seen an A1200 but better specced with Blitter and so on, things might have changed slightly but I think the Amiga platform as a whole was doomed to last much further than 1997 no matter who was in charge*. Microsoft would have made sure of that, along with the imminent Apple resurgence.
*Amiga as a commercial high-street product.
