My question was about AFC vs. AFS for taking pictures of birds, not about using flash.
Well, now you have something new to try!

I believe most hummers have some iridescent feathers, and the flash will light them up. It’s worth trying, if you care to.
First, put your feeder in shadow to reduce the light you have to deal with. You need a light stand to put the SB-600 on. It came with a table stand, so a ladder should work fine as well. Position the flash about 1 foot from where you expect the hummer to be. Using your image as a guide, I would put the flash head level with the bird position and to the right, just out of the camera’s view. Rotate the flash head (well, rotate the body) until the CLS wireless sensor (by the battery cover) is facing the camera. Follow the instructions in the SB-600 for enabling wireless mode starting on page 60. It goes something like this...press ZOOM and “-“ (minus) together for a few seconds to open the Custom Settings Menu. Then press plus or minus until you see the “wireless” symbol (that squiggly arrow.) Then press mode until the LCD says “On”. Now press the On/Off button to exit Custom Settings.
On the D7000 use Custom Setting “e3:Flash Cntrl for Built-in Flash” to enable the Wireless Commander. Page 225 describes how to set the Commander settings. Here’s the checklist for wireless flash...
1. Make sure the flash and camera are set to the same channel.
2. Make sure the flash is set to “Group A”. On the camera, makes changes to “Group A”.
3. After changing settings in the Commander, you must press OK. This is one that people miss.
4. Raise the built-in flash (another one people miss.)
In the Commander, set “Group A” to “M” for manual flash power, and then set the flash power to 1/128. You can also set the Built-in to "--". Your flash is set. Now set the camera to M mode, set shutter to 1/250s, aperture to f/11 and give it a try. Adjust aperture up or down a stop as you see fit. If you need more flash power, 1/64 should also work fine.
Good Luck!