No, the scheme shown will only work with the MAX5160 because it has Increment and Up/Down inputs, while the PGA has a synchronous serial interface that could be done in hardware with more effort.
The DS1802 mentioned in the other thread would work without a micro. But I don't know if either of these have zero-crossing detect like the PGA2310 does (I doubt it). Also, both the MAX5160 and DS1802 are limited to a +5V supply; the PGA has separate analog and digital supplies.
I believe somebody who had tried the DS1802 had trouble with its voltage swing.
Another big difference to me is that Burr-Brown and Analog Devices have done more audio-grade parts than Maxim and Dallas Semiconductor, so I trust them more.