YES, a bad fuel pump can make the vehicle idle low since it is not producing enough pressure for the engine to run smoothly as it should. Fuel pressure must be maintained within a generally accepted range of about 30-80 psi (usually dependent upon the vehicle) for most engines to operate correctly. If the pump is delivering less pressure than required, it may cause the engine to idle at a lesser RPM as there will be not enough fuel flowing and combustion rate becomes inconsistent. In older or high-mileage vehicles, the issue becomes more prevalent as fuel pumps typically start to fail after about 100k miles and the pressure can be all over the place.
When the engine does not get enough fuel at idle RPM it affects overall performance too. Most engines idle somewhere between 600 and 1000 rpm, but if the fuel pressure is too low that number could drop way down causing a rough or unstable idle. Most of the time mechanics will find out if this is what's going on through the use of a fuel pressure gauge, it tells them how well that pump is holding constant pressure. If the reading is below manufacturer specifications, it's very likely that your low idle condition has to do with a bad fuel pump.
And, low idle RPM can also elevate fuel usage and emissions higher as the engine struggles to maintain efficiency of combustion. The cost will add up, especially over time from excessive fuel consumption if the problem is not fixed. A faulty fuel pump can cost $400-$800 to replace, depending on the vehicle model; however it is a great way of cleaning up that chicken hearted flow and idle RPM in your car as its efficient for 10-15% better mileage.
In addition, the quality of fuel can also have an effect on pump performance as dirty gunk-laced (gummed-up) petrol will clog up a carburetor or clogged itself before other equipment like its filter and reduce flow causing slow idle RPM. To avoid clogging, you should fill your tank with high-quality fuel and change the fuel filter every 30,000-50,000 miles as mechanics recommend. As Henry Ford once said, "Quality means doing it right when no one is looking," this was a point to reinforce the importance of maintenance.
Is the idle RPM dropping — consider checking out your Fuel Pump. Check here Replacements for more.