This applies to all Interfaces and Preamps with Digital I/O
The answer is yes but with incredibly little latency. The minimum latency the human ear can detect is about 11ms. It would take between 10 and 20 stages of A/D and D/A before we noticed any latency in a signal.
When considering latency in your system, A/D and D/A stages are negligible - it is more the audio buffers for your audio interface and sampling frequency that you should be concerned with.