The ground strap shouldn't have any effect on the alternator, it has nothing to do with the charging circuit where the alternator and battery are concerned. Yes, it will make quite a difference for electrical components grounded to the body, but the alternator grounds through the engine block to the battery. Like 79loserbu said, check your voltage with the car running. If it doesn't read around 14v something is wrong. If it's not charging it will read anywhere from 8-12v. Yes, it will run on voltage that low, however poorly. If it's not charging, make sure you have voltage at the brown wire of the alternator connector with the key on. As you can see on the diagram, the brown wire is run through the 'charge' light, and if it has gauges there is also a ~10 ohm resistor. These are required to keep the regulator from burning up I believe. If there is no voltage, something is amiss in that circuit, I'd double check the charge light, and make sure there is a good connection at the light socket.
Doober said:
I tend to disagree with you and i'm sure other people on here will as well. I've had the same problem and as soon as i connected the ground strap to the chassis the problem went away, so i don't know where you got your info but if the alternator is grounded to the motor but the motor is not grounded to the chassis then you are going to have a weak charging system period! Just because the battery is grounded it does not mean that the engine itself is grounded which it definitely needs to be! Regardless of the cause of the problem, he definitely should hook up the engine ground strap or do you think he shouldn't>???