The Super Game Boy has received a significant upgrade with the introduction of the Super Game Boy Plus, an unofficial enhancement developed by @BucketMouseBite. This new version addresses several limitations of the original Super Game Boy, which allowed Game Boy games to be played on the SNES but had a faster clock speed than the original Game Boy, affecting gameplay and compatibility with link cables.
No, it doesn’t copy the game data in the way you’re describing, anymore than a Game Genie would (it doesn’t either).
And anyway, this Nintendo lawyer fear is getting a little ridiculous in this community. ROM dumping for this kind of data is legal, at least in the United States.