How can I tell if an appliance is grounded?
If you have a known good ground nearby (or can get one by using an extension cord), you can check that the appliance plug (if it has one) or its chassis has continuity to ground using a multimeter. 

In resistance mode (measuring Ω), you should read 0Ω (or very close).

Note that that will only tell you that it's connected, not that it's adequate for the load: the ground wire should be as big as the hot, because it will have to carry the current if it's ever needed. There's not a way to test that, that I know of, you just have to inspect the wiring. I'd definitely be highly wary of a random wire connected as you've shown being used as a ground.