Where the anime doesn't contract did the games, I'm fine with coopting that into my headcanon continuity of the series.
Madame Boss was never even alluded to again, though. She was most likely a single writer's idea and no one else cared for it.
Making Giovanni's mother the previous boss of Team Rocket is a lame idea, though, because it makes it impossible for Team Rocket to be something he build himself, from the (under)ground up. Instead it was handed to him. Headcanon, yes, because we don't know how Team Rocket was established, but nothing too out there.
