it is likely that 'goose bump' music tends to have a particular distribution of intervals, discordant harmonies, dynamics and key changes etc. One can imagine a computer being programmed with such rules and coming up with an effect piece of music, but with no knowledge that it was composing music; that is a parallel to a chess computer that plays at grand-master level but doesn't know it is playing chess.
The other sense of the question is whether a computer can manifest the internal subjective states (emotions?) of a human composer and thus feel the need to express itself through music.
The difference is the difference between 'Artificial intelligence' and 'Artificial consciousness'. To achieve the former today would only require a collabortion between an average musicologist and an average computer programmer - we have no idea how to even begin doing the latter.