So long as the recording and reproduction processes are faithful to the colors present in the original image
The faithfulnees is at the monochrome level. The recomposition, if done digitally, is impacted by the scanner, the working colour space, and the output colour space. color chemistry has unique set[1] properties (eg polaroid) while digital has far more flexibility [2]. From there is more a question of style than authenticty per-se.[3]
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[1] The colour is set once, and by the chemists. Kodachrome will not look like Velvia will not look like Polaroid, etc. You can digitally mimic these looks, however. As instagram has shown, to good effect.
[2] Non-destructive 16 bit editing, various colour spaces, etc etc.
[3] We have limited idea what colours look like on Mars, etc
There's no conceptual difference between this process and that of 3-color film photography, in which three monochrome silver-halide images subject to filtration are made, and the color is added in, during processing, chemically:
https://en.wikipedia.org/wiki/Color_photography#.22Modern.22...
Or NASA's various color photographs, most of which are created using three successive images through different filters (and that's for true-color images, rather than false-color images in which the finished color range is entirely an artifact based on EMR outside the human visual range).
Or for CCD-based color photography in which, again, intensity recording based on filtered sensors is presented by adding in the colors selected for by the filters.
So long as the recording and reproduction processes are faithful to the colors present in the original image, the colors are authentic. As authentic as anything that's a copy of an original impression can be.