possibly, most likely not. a 10W pv module will not produce 10w most of the time (rarely in fact).
There is more involved than just watts as well. if you have a good charge controller it will compensate and adjust the voltage but if not then the voltage matters as it takes a certain over voltage to even start to charge. You can not just trickle charge a lead acid battery either, so a 10w pv module even without an LED is not going to do much charging.
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