It can enough for a test if you have a headphone output jack, as can an MP3 player, computer, etc. What you want to know is are you able to get any audio out of the tweeter or is the coil blown. Keep the volume level LOW.
If you have an ohm meter, check the resistance across the two terminals. If it is functional, you should read a low resistance such as between 4 or 6 ohms if it is an 8 ohm tweeter. Any resistance is good. As I said above, the tweeter should be disconnected from the crossover when performing this test.
You may have heard of a battery test for speakers. DO NOT do this with a tweeter. The DC voltage can damage the tweeter.