No, I don't believe the Carter/Edelbrock is known for leaking it's fuel. For whatever reason I have a 2x4 425 set up which definitely does not have the problem.
Are you sure the choke is closed far enough before cranking. Also, just in case you are young and don't know, with a carburetor, you do not just climb in and crank the ignition switch. You must open the throttle a bit first to allow the choke to set, then crank. Some times a couple of shots of the gas pedal can help. You probably already know and do this, but start with the basics

So the problem could be fuel related. Looking around it seems modern fuels vaporize at lower temperatures. I always run premium grade fuels without ethanol. Maybe that makes a difference.
If the problem is vaporization, look at things like carburetor gaskets, they could make a difference. Either double or triple gasketing it, or using a carburetor heat shield.
Under-hood temperatures in general are going to effect the problem. Most header installations increase under-hood temperature.
If you eventually install an electric pump, I would choose to hook it into the ignition switch so that it only runs when the ignition switch is in the on or run position.
Here's a bit on fuel and starting:
http://www.thecarburetorshop.com/Troubleshooting.htm#Hardstartcold