The only way that I have upgraded myself and my clients without paying a fee is if the cruise rates of the higher cabins comes down to an equal or lower price than the cabin you are currently booked in.
With the large price difference that exists between Haven and non-Haven cabins, I have never seen that happen in the 10 years I have been doing it.
If Haven cabins are available near sail dates, NCL revenue dept will reach out to people to see if they will upgrade at a reduced rate. Most of the examples I have seen recently is usually mini-suites to Haven for $500-$1000 per person.