There should be no draw on the battery...it's the alternator that provides power to the vehicle. Batteries are only used when the alternator is broken, or the engine isn't running. I'm an expert recently on the former.
As it's been said...LED lights act completely different than incandescent bulbs.....prepare for computer mayhem when you start converting to them

. Conversion of s TV is a waste of cash. You'll never see enough gas savings to pay for them.
LED in the camper, if you boondock, is a different discussion. I personally don't like the light put out by LED bulbs for RV use...but they do produce almost no heat, and draw less current. If you can suffer the light quality that's a different use case, one where it starts to make sense for some. Even the warmest LED bulbs seem cold to me and there's an odd quality to the light....I'd almost call it a flicker, but DC current wouldn't cause that. It's harsh....I just can't get used to it. But that is just personal opinion.