Is there any source of entropy available to an NSF? If I, say, wanted to make an NSF that would play a random different tune each time, or a bunch of fragments that would be played in a random order...
NSF isn't supposed to have entropy apart from the track number (1-255). If you're making an NES ROM, on the other hand, there are ways to read entropy out of analog effects in the PPU: see
Pretendo.
NSF is very deterministic by design. As tepples says, the track number is really the only source of entropy available that adheres to the NSF specifications.
There may be non-deterministic elements available to any specific implementation of a player, especially hardware players, but to take advantage you would be building the NSF specifically for that one player. It would be very difficult to make an NSF that doesn't play the same each time on most emulators, but I expect it would be marginally possible on some. Any such effects are out-of-spec for an NSF, at any rate. Everything that isn't explicitly deterministic is forbidden, more or less. (State of the stack, the Y register at entry to init, A/X/Y at entry to play, use of PPU, reading the controller, use of IRQs, etc. may do different things on different implementations, so they are forbidden to be relied upon by an NSF.)
When I wrote my cover of Giant Steps, I put a random variation into the drum patterns to give them a little more life. The NSF version plays them the same every time, but the NES version increments the seed while waiting on the title screen.