The problem you'd have is a simple Markov chain would have trouble lining up the chord progressions on the larger intervals that chords line up on. You'd end up with a song that sounded sensible in the microscale but just sort of wandered around at weird intervals.
And if you fix this... well... you'd end up with chord progressions essentially indistinguishable from the sampled pop music. But that would be an awfully complex way to obtain results that you could just as easily do by hand. :) In fact many people can just vamp those chord progressions in real time if you don't expect too much creativity.
That's the problem that David Cope had trying to do a Markov-chain-based recreation of Bach, in one of his many experiments in that endeavor; just wanders and doesn't really sound like much, even if all of the n-grams are legit, because it doesn't produce any kind of phrase structure. He ended up with sampling based on hierarchical context instead, iirc: http://artsites.ucsc.edu/faculty/cope/experiments.htm
I did this a while ago to create an infinite music machine. The chains are just based off of one particular song (Bicycle built for two, which also happens to be the song the IBM 704 sang back in the day) but could be made to work with these chords (The site appears down, so I can't access the content).
