Why does the PQube 3 current channels show noise when nothing's connected?

This is normal. 

What you are seeing is either noise or a DC offset drift. It is not uncommon for instrument components to drift over time. And some will drift more than others.

As a matter of fact, all the current channels have a drift but the PQube 3 will zero it out based on a threshold. In AC, this is not a problem and will correct itself when you apply a load to the current channel.