Yes a low battery will draw more amps. With a charger we can reduce the amps a low battery draws by reducing the voltage of the power supply.
A photo sequence of that in
this post.
It's like a light bulb in that regard. If the lightbulb is connected to a power source at lower voltage, it will draw less current and dim.
When the battery is connected to the car's power system, the recharging voltage is somewhat fixed. The only limitation is the alternator's capacity to produce power.
As far as the alternator output goes, it only puts out the amps needed to charge the battery
and whatever else is running.