Yes, mathematically. But copyright requires copying, strictly speaking, so you need a copy from which to have copied.

An algorithm that generates all possible English sentences doesn't demonstrate that I copied this sentence from it, and the balance of probabilities (used in tort cases) suggests that I came up with the sentence, run-on as it is, rather than performing that algo and then selecting that sentence. Moreover 17USC (102? sorry I don't recall) says that media needs to be "fixed" to acquire copyright; so me having to perform the algo makes it no impediment to my owning copyright of a sentence that, if performed, the algo would by expected produce (which is sensible really, perhaps the algo is errant and can't make this sentence, maybe it only forms grammatical sentences ...

Does the algorithm represent the Kolmogorov Complexity of the dataset?

Of the "all possible melodies" dataset? Yes. Of the "all possible melodies humans would conceivably consider music, and nothing else" dataset? Not at all.