So that would give us 3x7 or 21 bits of color. 2^21 is a little over 2 million unique colors.
So with 10 million colors kicked around by human vision ( https://en.wikipedia.org/wiki/Color_vision ) you could ask if this is enough. I'm going with good enough as the color gamut ( https://en.wikipedia.org/wiki/Gamut ) of most displays don't cover the full human eye spectrum so in short, it's good enough.
How many different colors could be represented with an RGBO scheme if 7 bits were used to represent each RGBO component?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic