I can't say I've tried it but with my inverter (100W) the manual says, that you sure run the engine for 10-20mins every 3-4hours to stop the battey going flat.
But just in case the inverter has an auto-shutoff, when the battery is starting to go flat it makes a beeeeep noise for 5mins and if the engine hasn't been restarted the inverter shuts down to leave enough in the battery to restart the car. Neat!
As a general rule, it takes 10-20 minutes of driving to recharge a battery. Also, in most cars you can leave your headlights on for at least an hour or two before your battery dies, and I'm quite sure your car player will draw less power than that.
But one amp on 110 volts is about 9 amps in 12 volt out of battery.
Head lights are typically 50-60 watts each so leaving them on is pretty much same as playing mp3s with low volume, if your sytem takes like 100 watts. Plus if you are using inverter you can add some additional as power loss in transfer 12-110-12.