The 7800 actually had some pretty good games. Sure, some of them were...um...confusing and seemed pointless but, it did well with it's arcade ports and even a few of the original games that were released for it, once you figured out how to play them.
Believe it or not the 7800 was just an enhanced 2600 so, there's no way that a 5200 adapter would have been available as the 5200 (hardware wise) was the more powerful system.
The systems designated names sort of give it away as well. The 7800 is backward compatible *because* it is based on the 2600 hardware.
Want proof? Look it up.
The 7800 was the console that you heard about once in a great while but, probably didn't see or know of anyone who had one until the NES had already been declared champion of it's class.