Typically headlights consume no more than 55w each, although some rare HID's can require up to 72.
So - assuming your alt runs at around 14v your headlights draw about 110/14 = 8A.
So unless you have a 20A alternator (you don't, 60A is very small) your headlights won't have a significant impact on how fast your battery is recharged, but it will take a little longer than without them.
Actually - It's possible running the headlights won't have any effect on recharging the battery at all. Unless using the headlights + recharging the battery maxes out the alternator (which it shouldn't) the alt should just produce the extra current to power the headlights AND supply all the current to the battery that it needs to recharge. Worst case scenario is it will just take a few minutes longer.
Letting any battery go "dead" is a bad thing in regards to its' lifespan. Typically you shouldn't run any 12v batt below 50% DOC, unless it's a deep cycle battery.
