Yes, if the colours were pure you would get white.
Your other combinations aren't quite right:
Red and blue give magenta (the complement of green).
Blue and green give cyan (the complement of red).
Red and green give yellow (the complement of blue).
In various proportions you could get any colour you like. This is additive mixing as used in colour television -where you actually mix generated light.
Most colour we see is from paints, dyes and pigments where your three "artist's primaries" are cyan, magenta and yellow -the three inks in your computer printer - from which you can get any colour.