Edge can be used for running, but it's not an ideal solution.
First, you need to improvise a wrist/arm strap. One user reports having success using an iPod holster with a clear plastic front. Look for one that fits and has a window that's large enough to see the display.
Second, your training history will mix run and bike activity. This might make it a little more complicated to analyze your performance.
If you run and bike equally, you might consider Forerunner 305 with an optional speed/cadence sensor. If you mostly bike but occasionally want to use Edge for other activities, it's doable with a little creativity.