Leaving CD in receiver?

Absolutely.  Pioneer head units are pretty reliable and I've experienced hardly any problems in terms of stuck CDs, if that's what you were concerned about.

When you turn off the car, there is still power going to the head unit via the +12 volts constant wire.  All that happens is the +12 volts switched wire stops getting power, and so the main head unit power turns off.  However, it is still getting power via the constant wire so it can still make a note of what track/time it was turned off.  It always has time to park the lens and properly stop spinning the disc so you have nothing to worry about in that regard.

Now if your constant power wire is not hooked up properly then that's another story.  I don't know if it would necessarily cause damage but I agree that over time it just seems like it'snot the right way to use the unit.  But you would notice if your constant power wire was not functioning properly, because all your radio presets as well as the clock would all get reset whenever you turn off the vehicle.

Pausing a CD in general is completely different from pausing a VHS tape and there is no way to damage the disc or the player (at least not that I know of) by leaving a CD paused.