It could if the battery was so weak as to not be providing enough voltage to run the engine. But if that were the case you could not rev the engine without it missing badly. Drive to your nearest auto parts store and they will be happy to check your charging system free of charge.
A clogged muffler can.
sounds like the alternator is going bad.
Unless the battery is shorted or sulfated and will not take or hold a charge, most likely the alternator is bad
Bad catalytic convertor. Egg smell is a dead giveaway.
Check the voltage output at the battery posts with a multimeter set to DC voltage in the 20 volt range engine idling. You should get from 13.5 to 16 volts. Any more or less and the alternator is bad.
A bad alternator will make whats called a whirring noise. It could also make a low growl. This is just the bearings going bad. If your alternator is not supplying any power, it has nothing to do with noise typically.
bad/partially blocked catalytic converter. - kind of a rotton egg smell, right?
If bearings go bad on a alternator/ will make a grindind noise or long squilling noise.. but if only electronic's inside alternator are damage no noise wil be heard
Bad tires and bad alignment can cause the car to shake at certain speeds.
Bad engine cushions can make the engine shake. bad spark plugs cause malfunction as the car starts running.
Slipping alternator belt Loose connection Bad alternator Computer problem
Sounds like your alternator is going bad. The extra juiced used when breaking robs power from the other lights. Pulsing when idling sounds like the voltage regulator which is built into the alternator. Have it replaced.