Of course. Thats because the pokemon anime is almost synonymous with the video game series.
However, the f-zero anime isn't canon whatsoever. If you want to go even deeper into it:
the first reason is because, unlike the pokemon anime and games, the F-zero anime and games greatly contradict eachother. For example-
most obvious fact is that douglas J falcon doesn't exist in the anime. But for some reason, you keep on denying this fact.
Also obvious is that many characters are dramatically different from thier video game counterparts. For example, octoman in F-zero GX is a normal guy/alien who races to support his family and people. However, in the anime, he's an evil terrorist.
Also and the final stake in the heart in your little theory is the presence of black shadow in the anime. Since you keep on believing that Bart=Douglas, keep in mind that in F-zero GX, Falcon stays himself throughout the entire game. However, near the end of the game, black shadow is killed by deathborn. So if the F-zero anime took place before F-zero GX, then black shadow wouldn't be in GX. But if it took place after GX, Black shadow wouldn't be in the anime. GP legend just doesn't fit in the timeline.
And if you still need more convincing, Bart has an entirely different voice then Ryu/Rick. But SSBM falcon and SSBB falcon sound exactly the same. thread over.
also, the videogame with Ryu in it was based on the anime.