Is there some way to test an outlet to see if it's good and works without going through all the effort of installing it, like maybe with DC from a battery so that the LED lights? That may not be a true indicator, I realize, as the unit could be good, but the LED burned out, but it's a start, yeah?
An outlet is a very simple device electrically. An ohmmeter will verify that the front terminals (where the plug mates with it) and the screw terminals in the rear (where the wires attach) are connected. If that is OK and a physical inspection of the outlet shows no cracks or corrosion, then it is almost certain that the outlet is OK.
The problem with your little tests is that the outlet can/will react differently with the higher voltage and current that it's designed for. Outlets usually fail because the "jaws" become weak and don't grasp the plug tight enough. The other reason for failure is how they are wired. Using the back stabs instead of hooking the wires on the terminal screws can cause poor connections and failure of the outlet. Outlets are very inexpensive and easy to install. Just pick one up and install it. Remember to turn off the power before doing any work and take a few pictures before you disconnect anything so you can post them if you run into problems.. Good luck