Correct, but if the system is full, most will start even with a duff pump.
Where exactly is the buzzing coming from? Left or right of engine bay when you stand in front looking at it?
I'm wondering about the fuse box, many problems originate there, bad connections/duff relay causing shut of valve to buzz but not open for example.
As long as your bypass is airtight it will cause no problem. The fuel heater probably doesn't even come on unless the air temp is below zero and many cars do not have them.