ADN8810 control frequency from Arduino Due
The maximum SCLK frequency, according to the datasheet, is 12.5 MHz, and a transfer takes 16 bits, so that limits your update rate to (12.5 / 16) MHz = 100 MHz / 128 = 781 kHz to begin with.

You have a settling time of the output of 3 µs, so, if you need accurate output after every time you write, that's take 16 / 12.5 µs + 3µs, but that's just latency; your effective possible rate of accurate change is 1/(3µs) = 333.33 kHz.

When you look at fig. 13, you'll find that the output impedance, however, starts drastically changing after ca. 1 kHz, so whether or not that works for you: depends on what you attach to it.

Regarding the Arduino Due: I'm not an Arduino expert, but an 84 MHz ARM Cortex-M3 like used on that board should do a couple MHz of SPI rate, easily. I don't know efficient the Arduino SPI library is – it might or might not be simple and close to the metal – but software is easy to replace; FreeRTOS runs on the Arduino Due, so you won't be maneuvering yourself into a development dead-end if the Arduino software platform doesn't work.