Should you be able to hear your fuel pump running constantly? It seems like most cars you hear the pump prime but then you don't hear it. But I didn't know if the pumps on blazers are just like that. Btw it is a 2000 blazer

 

With no noise, you should hear it prime. Once the engine starts you shouldn't hear it over the engine noise.

Typically when you hear the pump run, its an early indication its about to stop working. How long it will last depends and there is no hard fast rule.
The pumps are internally cooled by your gas, if your always driving on E, the gas gets hotter, and you wear the pump out faster. We have a closed loop system, in that the pump pushes more gas than the engine can use, the excess fuel returns to the tank via a return line. If your pushing the same gas to the engine and back its bound to get hot. The hotter it gets the hotter your fuel pump runs, the hotter the pump, shorter its life span. The more the internal parts wear the louder it gets, until one day it dont make any noise and your searching the boards for the DIY Sticky on how to replace the fuel pump.

 

Yea that's what I figured. It's just painful to pay the 370 the autoparts store wants lol