Just tried, and the same trick works for Illustrator as it does for Photoshop when snatching a color outside the window. Here's what you do.

  1. Arrange your windows so you can see both your Illustrator window and Photoshop window at once
  2. Select the eyedropper tool in Illustrator
  3. Click on the Illustrator window, and WITHOUT RELEASING THE MOUSE BUTTON, move the eyedropper over to the photoshop window and the color you want to grab. See how the Illustrator color keeps changing as you move.
  4. Release the mouse when you're over the color you want.