The answer is "maybe". The load on the alternator, and rating of the alternator, is going to play in here.
The lighter socket isn't going to be rated for a lot of amps, so if the battery is just being maintained, not charged, it will probably be ok. As mentioned, you wouldn't want it INSIDE the vehicle while charging.
What kind of usage are you looking at? One night? Multiple nights? Realistically an alternator is not made to charge the batteries, only maintain the charge. That said, replacing an alternator slightly more often than normal is cheaper than getting a generator just to charge a battery.
I had considered this for an electric boat motor, and will probably use the vehicles charging circuit to help charge the battery, but will definitely be using solar to do as much charging as possible.
Edit: Right...I don't know anything about this...like you should be running 12AWG for 10+ amps on a 12V system? Which you clearly don't know, or you wouldn't say you could do it. You've never taken a car wiring system apart have you, or you'd know that the wiring to the cigarette lighter is nowhere near 12AWG.
How about the alternator? You know what it's rated for, and what it's load is, even though we don't know what vehicle this is? I suppose because a cold start somehow increases the load on a battery vs. say idling in traffic in the summer with the AC cranked, and electric fans buzzing, trying to charge a secondary battery through too-small wiring?
Additionally, your dangerous assertion that sealed batteries don't vent is borderline abuse of yahoo answers. "Leisure deep cycle batteries are all (I think) sealed so no you won't get explosive gasses." Yeah, go ahead and find me a sealed lead-acid battery that can't/doesn't vent. Maybe you mean AGM, but you obviously don't know enough to say that.
So you don't waste any of your precious time doing any discovery learning, here are two links to refute your dangerous and incorrect assertion:
http://www.carquestprofessionals.com/batteries/faq_myths.html#9
http://nuclearpowertraining.tpub.com/hdbk1084/css/hdbk1084_22.htm
If you want to trust your/passengers lives to an electrical component that eventually WILL fail (a battery) on the assumption that it will never fry due to internal problems or a charger issue, you are beyond help.
And WE don't know anything about this?