Most instruments generate harmonics that are integer multiples of the fundamental frequency, and some go a lot higher than human hearing. As you go up the harmonic series, the harmonics get (logarithmically) closer together. Our brains interpret close-together notes as dissonant, so higher harmonics could be kind of obnoxious to hear together. They might be "in-tune", but just too close to be enjoyable. (Imagine an extremely bright harpsichord.)
There's another effect that comes into play, though. There's a minimum pitch separation between simultaneous notes that we expect, and when notes are closer than that, they clash. That separation is usually around a minor third (~300 cents) in most of the human hearing range, but in the bass it's a lot wider, and in the high treble it's smaller. That's why you can play two notes a major second apart (~200 cents) on a piano in the high treble and it sounds okay, but down in the low bass it sounds muddy if they're closer than about a major third or perfect fourth (~400-500 cents). So, if we extrapolate into higher frequency ranges, then it's not unreasonable to expect that we would be able to interpret musical intervals that are a lot closer than 200 cents as consonant.
It's also possible that the minimum note separation thing is just an artifact of how our ears physically work, and that an artificial ear would have no such limitation. Which could open the possibility of enjoying kinds of music that we can't currently imagine as pleasant with our normal ears.
Because of the power decrease as you go up the overtone series, I'd suspect that being able to hear higher frequencies wouldn't cause very much trouble. However, the ability to hear higher fundamental frequencies would surely change harmonic theory! This is assuming that our pitch perception of high fundamental frequencies increased accordingly.
There's another effect that comes into play, though. There's a minimum pitch separation between simultaneous notes that we expect, and when notes are closer than that, they clash. That separation is usually around a minor third (~300 cents) in most of the human hearing range, but in the bass it's a lot wider, and in the high treble it's smaller. That's why you can play two notes a major second apart (~200 cents) on a piano in the high treble and it sounds okay, but down in the low bass it sounds muddy if they're closer than about a major third or perfect fourth (~400-500 cents). So, if we extrapolate into higher frequency ranges, then it's not unreasonable to expect that we would be able to interpret musical intervals that are a lot closer than 200 cents as consonant.
It's also possible that the minimum note separation thing is just an artifact of how our ears physically work, and that an artificial ear would have no such limitation. Which could open the possibility of enjoying kinds of music that we can't currently imagine as pleasant with our normal ears.