"I think that the on-or-off stepped triangle channel with its prominent 32x overtone is the signature of NES music"
Almost. Several Game Boy games, such as Tetris loaded the NES triangle waveform ("0123456789ABCDEFFEDCBA9876543210") into tone generator 3's wavetable; in fact, my GBA music engine has it as the default waveform for tone generator 3. The thing that sets NES audio apart from Game Boy audio is the ability to do soft envelopes on the pulse and noise channels. The Game Boy allows for a hardware envelope with an initial volume and a decay rate, but channel 1, 2, or 4's volume can't be changed without starting a new note and incurring an audible click.