There's a leaked memo about this deal available here: https://web.archive.org/web/20080327135150/http://www.atarim... . Atari had already paid General Computer to design the 7800 when Nintendo reached out to them about distributing the Famicom. Atari viewed the 7800 hardware as likely being superior to the Famicom, so their strategy was to string out the negotiations for as long as possible until the two systems could be directly compared. The Coleco Adam dispute was probably just a convenient excuse to continue delaying.

When Ray Kassar was forced out due to insider trading (he sold a bunch of Atari stock around half an hour before Atari reported much lower than expected earnings), the business press was generally dismissive of the idea of introducing a new console into an already oversaturated market. The 7800 ended up getting delayed into 1984, then Jack Tramiel bought the company and didn't want to pay General Computer royalties on the consoles or software so they sat in a warehouse until 1986 when Atari finally paid up.

If Atari did end up going with the Famicom instead of the 7800, I imagine it would have ended up delayed and hamstrung the same way the 7800 was. If anything, maybe this would have left space for the Sega Master System to take over in the US.

We'd exchange those handhelds with other kids & play 'em to death. Plane & Tank Battle, Highway and Q-Bert spring to mind as some favourites.