It is not just the LED that is being powered. The rest of the charger is as well. And depending on the build quality of that charger, which parts they used, which parts they didn't use, etc, it can vary.
On the low end, a few mA for the LED itself, and a few µA for the switching regulator charging circuit (quiescent current). On the high end, 20~30mA for the LED, a few 10s of mA for an inefficient LDO, badly designed passive parts, you might be looking at 100mA or more.
AND THEN there is the phone dock. Is it just a empty plastic passthrough dock, or is it an active dock with features and stuff? If it's the former, it's basically just a cable. If it's the latter, it's a load on the charger, and that means an increase in current draw.
Only way to tell the actual draw is by using an ammeter or multimeter to test it.
As for affecting the battery, it highly depends on your battery's condition. If you do a lot of short 3 minute trips in one day, you quickly drain the battery. If its years old, it's capacity might be drained. There is no single answer. Consider that in my Camry, the map light is 200mA. On my old battery, leaving that on for 10 hours will make me need a boost. On the new battery, leaving it on for 14 hours didn't even make the battery strain at starting this morning.
In short, there is no one answer. Either use a switched cigarette outlet or chance that your battery might drain