No the EGR will not open without a vacuum signal.

My initial thoughts; vapor locking, idle mixture too lean, idle speed set too low, float level in the carburetor too low or the float has saturated and sunk.

Also, you can try this. When it stalls out, pull the air cleaner and manually hold the choke partially closed (about 3/4) and have someone try to start the engine.

It does sound like a fuel system issue.