I was wondering if an electric fuel pump can still be running (makes noise) and yet be "bad", as it not being able to pull fuel from the tank.

Most pumps are not designed to pull fuel, closer you mount near the tank the better.

Also check to see if its ran properly, there are IN/OUT ports - Just assuming since I can't see with my own eyes :D

Electric fuel pumps are pushers, not pullers. Supposed to be more efficient and reliable.
I would check for fuel pressure. Do you have fuel pressure gauge? I put one on my carb inlet line for this purpose.
There should be a fuel filter between the gas tank and the pump, check it, maybe it's clogged.
I seem to remember my electric pump growing quieter (sounding weak) but still pumping fine, right up until it suddenly died on the road. Guess that was the warning sign I didn't heed.
I don't care for electric pumps, too noisy and expensive. Mechanical fuel pumps are plenty reliable for the street.

Fuel filter is probably the most common reason for not having normal fuel pressure. An electric pump can also leak internally. Fuel filters are usually cheap and easy to replace do that and if you still have a problem start looking at the pump as the problem