Yes, you're correct about this sentence. The way the sentence is written indicates that the bill was eventually paid.
If the author had written 'has gone unpaid' we would understand that the bill still has not been paid. The same verb tense could also be used in the case where it has just been paid, immediately prior to the current time or at the current time. If used for this second case I would expect there to be some reference to the changed status of the bill in the expression to make it clear, either implied by the tone or expressed in words.
...has gone unpaid for more than 50 years, until now.
...has gone unpaid for more than 50 years, and finally the wait is over.
...has gone unpaid for more than 50 years. It's amazing it's been taken care of!
Are you sure the first phrase in your example wasn't, 'As it turned out...'? It doesn't make sense to start that sentence with, 'As he turned out...'. The phrase, 'As it turned out' means, 'It became apparent that', or 'It was realized later that'.
It became apparent that much of the bill owed for the recordings went unpaid for more than 50 years
The phrase, 'As he turned out', could mean a physical turn, as in
As he turned out of the driveway and walked down the street
It also has a less common meaning
As he showed up.