A profile can certainly define some (R,G,B) triplets as "colors" which cannot be displayed on a particular monitor or printed by a particular printer. Can it also define "colors" outside the range of human vision? Or is there some definition or convention which limits the color space which can be defined by a profile?
See
https://en.wikipedia.org/wiki/ProPhoto_RGB_color_space.
Look at the 2nd figure down (click on it to enlarge it if necessary). You can see that sRGB and Adobe RGB are both fully contained within the gamut of human colours, so all possible RGB combinations of values for these colour spaces fall within the range of human vision.
ProPhoto RGB goes beyond, but as Andrew says, values that lie outside the gamut of human vision aren't colours. That doesn't mean they're ultra violet or infra red or whatever - values outside the horseshoe shape don't represent any wavelength or combination of wavelengths. They're mathematical anomalies, if you like.
It's rather like talking of a temperature of -1 Kelvin. You can write down that number, but it doesn't represent a temperature, as temperature can't physically go below 0 Kelvin.
