Suppose we are able to stimulate the whole matrix of cones of a human retina, targeting each cone individually¹. Normally we would project an image in the LMS color space onto the cones, in such a way that each sub-image of particular color channel would get to cones of corresponding type. As the eye moves, this image would be adjusted so as to create an illusion of real surrounding (similarly to a VR headset).
Suppose now we think up a new spectral sensitivity function $P(\lambda)$. We choose a subset of e.g. M cones to represent this type of sensitivity, making sure that this set is scattered enough around the M cones so as to avoid clumping the same color channel cones. And then we try to simulate tetrachromatic vision by replacing the M-channel sub-image in the projection by a special sub-image that an actual sensor with $P(\lambda)$ would capture.
Would this result in a sensation of a new color having appeared in the image, or would this be simply a lot of noise in the visual field?
¹The technology is not quite there, but on the way: see e.g. this answer.