Question, would a 4 watt bulb affect the charging vs a 2 watt stock bulb?
Yes. Note sure how well I can explain this, but I will give it a try. The alternator light that indicates low voltage from the alternator is actually part of the circuit that the alternator uses to determine how much current to send into the car to cover the current being consumed and to charge the battery. When the current flow from the battery side of the circuit exceeds the current flow from the alternator, the alternator increases its output to match. The alternator determines this current flow using voltage received from the battery and Ohms law (voltage/resistance = current), with the resistance employed being the sum of the resistance in the wire from the battery to the dash bulb plus the resistance of the bulb plus the resistance of the wire from the bulb to the alternator. When you replace an incandescent bulb with an LED, you are changing the resistance of this circuit. This then gives a false signal of current usage to the alternator causing the alternator to output the wrong current.
If the LED bulbs have much lower resistance than the incandescent bulbs, the voltage flowing from the battery to the alternator would be higher signalling to the alternator less current usage than is actually occurring in your car and less need to charge the battery.