Keeping the engine running is a good idea, especially if you don't have the recommended Aux battery for winching. (Or wenching.)
Consider, the 4,500 winch can draw over 200 amps at full load - winding in a slack line takes 30! The alternator, with the engine running at 5,000 rpm, can make about 50 amps, the engine, with all it's smart stuff, will take some of that, leaving some to help the battery . . . but in NO WAY can it keep up. If the engine is at idle, the alternator is putting out much-much less. And you may be in a situation where you need to winch but cannot run the engine.
Bottom line, if you are going to go interesting places with your P1000, it's very advisable to have an Aux battery and a winch. The Aux will help preserve your main battery to get you home AFTER you get your machine out of whatever predicament you were bright enough to get yourself into! It's like insurance. Or as Dirty Harry said, "Do you feel lucky, Punk? Well do you?"