The p0171 is usually caused by a vacuum leak or fuel pressure problem.It can lso cause the misfire codes.There are also issues with the coils failing on these cars .You can swap coils for 1 and 3 cylinders to 2 and 4 and see if the codes goes to 2 and 4 cylinder misfires if so those coils are bad.

Exhaust system

• Exhaust system components, removing and installing. See: Engine, Cooling and Exhaust\Exhaust System\Service and Repair

Fuel injectors

• Fuel injectors, checking. See: Component Tests and General Diagnostics\Fuel Injectors, Checking

Fuel pressure regulator and residual pressure

• Fuel pressure regulator and residual pressure, checking. See: Component Tests and General Diagnostics\Fuel Pressure Regulator and Residual Pressure, Checking

Fuel Pump (FP)

• Fuel pump, checking. See: Component Tests and General Diagnostics\Fuel Pump Checking

Intake system

• Intake system for leaks (unmetered air), checking. See: Component Tests and General Diagnostics\Intake Air System, Checking For Leaks (False/Unmetered Air)

Secondary Air Injection (AIR) system

• Secondary air system for proper seal, checking. See: Component Tests and General Diagnostics\Combination Valve For Secondary AIR, Checking Function and Proper Seal

No that will not cause a rough idle it will usually cause a stalling issue or fluctuating idle.What I stated is what will usually cause these issues and is what you should check first .Unless it jumped times these need to be checked first.Hoped this helped.

Positive feedback and bonuses greatly appreciated.

No it's not supposed to let you in these ate the issues that it can be .