What determines if a particular DAC is "good" for audio?
The AD5601 allows data bits being sent at 30 MHz, each packet takes 16 bits.

\$\frac{30 MHz}{16}=1.875MHz\$. 

That means that you can theoretically make waveforms up to the Nyquist frequency which is \$\frac{1.875 MHz}{2} = 937.5 kHz\$.

\$937.5 Khz &gt; 8kHz\$

The slew rate is 5 V/µs, that means that if you got a signal bouncing between 0 and 5 volt, a sine wave of 1Hz of amplitude 2.5 V has a maximum dv/dt at sin(0) => dv/dt = 1*2.5V => 2.5V, so a 2Hz sine wave got a dv/dt of 5V at t = 0. 
5V/µs => X/s = 5*10^6/s, so 2Hz*10^6 => the slew rate supports a whopping 2 Mhz sine wave. 
 

So yes, you are correct. That DAC is good enough for making sine waves sampled at 8kHz. What you said, 125 µs and 10 µs, together with the data speed &amp; slew rate => why I said you were correct. 

But let's reverse the formula, say you want to output what you sampled. 

\$8 kHz × 2 = 16 kHz\$ 

\$16 kHz × 16 = 256 kHz\$ 

This means that you need to send one bit every \$\frac{1}{256 kHz} = 3.9 µs\$.