1998 Ford Taurus Dies At Low Idle?

1998 Ford Taurus I know needs new alternator because battery won't stay charged.

When I boost the vehicle off it will run at 1000 RPMs smooth. No vibration.

As I lower RPMs below 1000 it begins to sputter almost like it's missing. Eventually will die completely.

Could the alternator not keeping charge to the system cause this? If not what could be other problems?

Yes. The fuel pump is electric so when voltage is reduced by a bad battery or alternator, less fuel pressure will be present so the engine will eventually stall. If the pump supplies 40psi when correct voltage is present, it will supply less pressure when voltage is low. If you measure across the battery terminals when the engine is off, a fully charged battery will read 12.75 volts or higher. If voltage is below 12.2 volts, it has to be charged or replaced.Read through the link below to learn how to test your alternator.
http://ricksfreeautorepairadvice.com/test-an-alternator/

It could be the distributor out of time with the motor, the spark plugs/wires, or the coil packs, or a tooth out of time, or the alternator.

Very low voltages can affect computer operation since it relies on micro-volt readings… Or the fuel pump could be affected if voltage drops too low. But the voltages would have to drop pretty low for them to be affected. Perhaps test the battery/charging system voltage at idle/low rpm's and see what the readings are… Parts stores or home centers sell low cost versions of DVOM or multimeters for around 10-15.00 for testing… A fully charged battery should be around 12.6-12.8 volts with ignition off and a deeply discharged one will read around 11.9 -12.1 volts. Anything below 12 volts can affect computer or fuel pump operation although it would take much lower voltage to affect the pump speeds. With engine running, the voltage from the alt should be around 13.5 - 15.3 volts for proper charging.

Another possible cause for the stalling issue is a dirty or bad IAC which the computer uses to regulate idle speeds by bypassing air around the throttle plate and adjusting injectors firing and timing. The IAC can be removed and clean the plunger tip as well as the bore it sits in with some spray Throttle Body cleaner sold at parts stores. Might want to clean the throttle body throttle plate area as well of soot /carbon deposits which can cause idle issues/stalling if low speed air flow is affected or the throttle plate does not close properly due to carbon buildup… Both should be cleaned as part of normal maintenance every few years or so. Reinstall IAC and retest… The IAC could still be bad and result in stalling issues and may not set a check engine light… Have to test for proper operation. Also a good idea to run some Seafoam or Techron in the fuel tank per label directions to clean injectors… Sold at parts stores, etc… Which can cause rough running from bad spray patterns/fouled injectors.

Links on cleaning IAC…

Battery tests…
http://www.aa1car.com/library/2003/us20310.htm