Yes, the injectors have power supplied when the ignition is on, and the PCM pulses the ground, the transistor can be bruned out, causing the ground to be switched on at all times.
Its really easy to find the culprit with a fuel pressure guage if the check engine light hasn't come on yet. More then likely its in cyl.'s 4-6 (left bank).
If you unplug all the injectors on the driver side bank, hook up a fuel pressure guage, turn the ignition on (don't start it), verify the fuel pressure is holding (usually 30-40 psi), then one by one plug in the injectors on the left bank while you monitor the fuel pressure guage. As soon as the pressure drops off, note which one you plugged in, more then likely that driver in the PCM is burned out.
90 LX, Previous 4 cyl.
408W In the Works
TW FAC's, Jay Allen cam, Super Victor
2001 V6 5 Speed Daily Driver
Windstar Intake, Dual Exhuast, CAI, Headers
Best ET: 15.44@91 mph (on 18's)