I have a hunch that I'm on to something here...
Be careful when you get off it then!
I've had cold start problems ever since I've had my GTI, where the engine stutters then finally fires up...sounds like a bubble of air going through the fuel lines.
I'd be curious to find out if all those who can hear the in-tank pump priming have ever experienced this delayed cold start issue?
My GTI occasionally stutters or hesitates on startup (usually when its been left for more than a day or two) - but I always hear the fuel pump prime when I open the drivers door. I also hear it do the same on my RS4 - and that is the same - starts instantly when used regularly, but if it hasn't been used for a fortnight or more, the starter can sometimes crank for about six seconds before the beast awakens.
Try removing the rear seat squab - because the low pressure lift pump is basically under the rear right seat - and then see if you can hear it. Or how about trying a 'double prime' - unlock the car, open drivers door, shut door, open drivers door again . . . and see what that does.
Personally, I'm not convinced at all that the low pressure lift pump is the problem - this does NOT provide the necessary pressure to activate the injectors. The electric lift pump is designed to pressurise the fuel lines to 6bar, whereas the mechanical HPFP will give around 110bar - and it is this 100+ bar figure which is needed by the FSI system. If your lecky low pressure lift pump didn't work, then it is doubtful your engine would run at all.
Finally, the electric low pressure lift pump is DTC enabled - it will log and store fault codes - so scan your car with VCDS.