Does analoge-to-digital conversion cause latency?

The answer is yes, but a very small 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 percieved 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.