What will cause my float bowls to go dry

This is exactly what I do on my street driven cars - leave the mechanical pump in place and add a small electric VANE STYLE pump in the fuel line toward the back of the car by the frame rail. The mechanical pump will pull gas through the vane style pump with no problem. MR Gasket offers a nice compact one that they have been selling for decades. I turn the key on, hit the toggle switch under the dash and count to 20, turn off the electric pump and they start right up.
Do you have a link to the pump that you are referring to? I can't touch gas without spilling it :)