As a "colorblind" person, this is a bit frustrating so bear with me.
Few people are literally "colorblind". You don't have one cone cell of each type, you have loads of them. Colorblind people generally have fewer of them (or some of them are shifted) but usually only for one type (usually red/green).
The "red" and "green" cones overlap quite a lot[1] and they also overlap with the rods. This means that even if you lack some "green" cones you will still likely perceive "green" colors, except they will be hue-shifted into red and less saturated. Simulating this effect for people with normal vision usually results in "muddier" colors.
Your analogy is pretty good otherwise (except as someone else pointed out, that's apparently not at all how the signals are processed) but this seems to be a widespread misconception about color "blindness", so I felt it's important to point that out.
It's also worth mentioning that it's meaningless to say "there's no such thing as pure green". Physically isolating certain wavelengths produces a "pure green" light. What someone with normal color vision perceives when they see "pure green" light is the result of multiple cones being stimulated at the same time, sure, but there's no one-to-one mapping of cones and colors except for some very small bits at both ends of the spectrum, which is why the cones are generally referred to as L/M/S (for long/medium/short wavelengths) rather than R/G/B (for the colors).
A tetrachromatic person (assuming the fourth cone type's peak sits somewhere between 420nm and 564nm, i.e. "blue" and "red") likely won't enable someone to perceive colors outside that range. In your example, the 3 people are forming a lopsided triangle. Adding a fourth person makes it a four-sided polygon but doesn't add another dimension. Tetrachromacy (depending on where the cones lie) would make it easier to distinguish certain shades though by making them more vibrant -- to them, normal vision would appear as "muddy" as my vision does to someone with normal vision.
[1]: https://commons.wikimedia.org/wiki/File:Cone-response-en.svg
EDIT: Because some people find that interesting, here's a page with a bunch of photos that fairly accurately simulate my color vision (i.e. looking randomly at both sets of photos I wouldn't be able to tell you which one is the original): https://web.archive.org/web/20160308043950/http://critiquewa... -- apparently brown skin looks green to me.
