Will QEDs block a ship from switching into Nav Mode?

Switching into Nav Mode, no, but it will block the positive effects from being in Nav Mode. So if you run a QED device, you will not enjoy Nav Mode speeds, but you will enjoy the lack of shields. So yeah, you can always switch the modes, but the effects are the ones that will be inhibited.

So you can be in Nav, but it's not really doing you any good.

Yeah. If you're getting attacked and you're in Nav, you have an incentive to swap.