Say I had a light source of exclusively 635nm, 532nm, and 473nm. Any idea as to the CRI that would have?

The only lamp that i know that produces exclusively 3 peaks in the red, green and blue and not any other colors in the spectrum is the RGB LEDs. But when they operates on White color, their color is, i think, inferior for general lighting then white LEDs based on a blue InGaN and a YAG yellow phosphor which have 75%-80% CRI. But RGB LEDs better for LED lit LCD TVs and computer screens then white LEDs.
Triphosphors fluorescents designed to produce red, green and blue peaks, but they have also in the orange, yellow and cyan.
Triband MH lamps produce three peaks. In blue and green, but in orange instead of red and in different wavelengths, not the note the mecury lines and the continum background.
CRTs and Plasmas also produce RGB, but they are based on wide band phosphors. Only the red one have a narrow band.
Your light source were probably RGB LED or similar to this.

My guess would be no more then 70, but it strongly depend on the ratio, feeding each LED with equal current is by far very poor (my guess less then 50; blue tend to be relatively too efficient and red too inefficient)

Isn't the green LED the most efficient? But I agree for the blue though. They would have to have equal lumen output to make a true complete spectrum, more or less. Those RGB LEDs works with the same principle used in triphosphor fluorescents, producing a complete spectrum with the three basic additive colours.

Do not mix radiated POWER with LUMENS, the "conversion factor" differ more then a decade for different wavelength

Green efficiency: Green LED efficiency is quite poor. But be aware, do not mix efficiency with efficacy. For same efficacy you suffice with ~10x lower efficiency for green compare to red.

And for white light you need same output POWER (and not LUMENS) across the spectrum. That is the reason, why 150lm/W of CRI99 white light source would be on the border of the "perpetuum mobile" device, while with CRI~80 we are talking about maximum 50% (it depend, what part of the spectrum is sacrificed) of input power wasted as heat and with monochromatic green we are with about 75% of input energy wasted as heat.

So for RGB source it mean, you need about 1/3 of power for each wavelength, even if the green is responsible for the majority of lumens, the other two you need simply to achieve the color. And most noticeable it is with the deep red: Even if it carry only about 3% of the lumens (while count for 30% of radiated power), it lack has major impact for perceived light quality...

Yes, I'm aware of efficacy/efficiency of different LED colors.

But I'm assuming PRECISE monochromaticity (is that a word?) ie +/- 1nm and well balanced amounts. You think that'd be CRI 70?

The only source that can produce an RGB spectrum of monochromaticity spectral lines, is by using three lasers: Red, Green and Blue with well balanced amounts, and a device that blends their emission and produce the overall color. The "white" light that will be produceted will be of very low CRI of perhaps 15%-25% since the specturm will be lack: only three lines of 1nm width.
Triband MH lamps produces 70% CRI because the lines are wide enough and the mercury line and the molecular continum, contributes to the spectrum.
Triphsophors fluorescents have a 85% CRI because the the RGB peaks are also not too narrow, and there is additional bands in the cyan, yellow and orange in addition to the main RGB.