If the engine is running, you will have the max capacity from the alternator, plus whatever current capacity the battery has in it at the time. Yes, it will take a decent load off the main battery when you're running the winch - but then the alternator will re-charge it once the winch load is removed.
If you had say a 100AH battery (to keep the example easy) it in theory could supply 100A of current for 1Hr before being completely discharged. Again (loose) theory says if you drew 200A from it, then it would last half the time - so 30mins. Whilst the battery would obviously not be the happiest about it, and in reality it wouldn't work like that - and you would have the engine running - so some power coming from the alternator - a winch would be fine on a single decent battery.
In fact none of the LR accessory fitting specs for the winch tray show fitting another battery or the need for it. For occasional winching the standard setup would be fine.
If you have a split-charge system and 2 batteries, then you're just upping the capacity - less stress on the complete system, and you'd be able to winch for longer if necessary.
As an example a Warn Zeon 10s 12V winch specs (from here: Warn Winch show that just running the winch with no load will draw 62A, and at full load will draw 409A. Given that's a 10000lb / 4536kg rating for the full load, you're never likely to pull that much - or if you do because something is really stuck, it would be for a short period. And if you were really stuck - you'd probably use a snatch block to double the line and make it an easier pull for the winch in the first place.
I added the second battery to mine with the view to fitting a winch in the factory winch tray that I got my mitts on awhile ago - and also to run other accessories like (now) my inverter and also the EAS compressor runs off it, so I can run that without the engine on and without draining the main battery.
If you're planning on making it so you can put a winch at the back of the vehicle, then having the second battery there gives you a good place to hook into it, and means you can probably do light winching without having to have the vehicle running - if it's a beefy enough battery!
I put my split charge system in with 230A (from memory it was over 9 years ago now) twin (+ve/-ve) cable from the engine bay to the loadspace. The +ve feed is fused at each end with a 200A (again from memory - might be 250A) mega fuse.
I think Sloth fitted his VSR/second battery with just a +ve run and then attached the -ve back to the chassis somewhere at the back. It's definitely more than capable of handling the current. I just ran twin cable in mine as it wasn't that much more expensive, and at the time I had all the looms out of the sill on the RHS, so was easy to run them in at the bottom and then lay the vehicle looms back over the top.