No - the 500 doesn't know whether you are riding or running so the calorie counter will run regardless. You can create a new bike profile and set the bike weight to 0 or 1 pound.
The problem is that the Edge will think you're still cycling, and if you run at say 10km/h, it will think you're riding very very slow and under-calculate your calories drastically - even with an HRM.
The old Forerunners allowed you to switch between cycling and running mode for this very reason, and would calculate calories based on the actiivity you're doing. But the Edge was designed strictly for cycling and doesn't have that feature.
I have an Edge 500 on the bike, and a forerunner 110 (one of the newest ones). Both sync up to my HRM at the same time. So I can ride, jump off my bike, push start on my forerunner, and run. Then I just add the calories at the end.