Should I leave outlet covers on or off for electrical inspector?
In many jurisdictions, there is a separate rough-in inspection and then a final inspection.  

The rough-in is usually done with wiring in place and before drywall is installed, unless the new cabling has been snaked into place.  Wires are exposed in boxes and no devices are installed in the boxes.

The final inspection is usually done with all devices and fixtures in place, and covers on.

But local practice varies, so your best bet is to ask the building department. They are usually happy to advise, assuming your locale allows DIY.