I used to train with a couple of guys who were powerlifters, and then moved on to the World's Strongest Man stuff. The thing I noticed with them was that they were out for brute strength, full stop. They did not care about being ripped, fake tan, and poses, just sheer muscle mass. So they ate for that, and trained for strength. They had a lot more body fat than I did, but then they did not care about that issue to the degree bodybuilders do. It is probably worth noting that a lot of bodybuilders adopt some level of powerlifting regime into their off season training to help develop muscle mass and increase strength. Strength comes down to diet, training and recovery in my opinion, and is not directly related to body fat. The only reason you see powerlifters or Olympic lifters carrying more body fat than a bodybuilder is that in those sports you are not judged on the appearance and definition of muscle, just on the amount lifted. James.
True, powerlifters aren't exactly built like Arnold. But they train and eat in abundance and consequently have a ton of muscle beneath their fat. I'm still under the impression that calorie consumption beyond maintenance level without training does add a degree of strength in some way - perhaps you do gain muscle along with the new cat, though certainly not the sort you'd gain if you threw lifting into the equation.
The average "fat guy" may gain some strength after binging on donuts but probably not much. For a trained individual a few extra pounds will definitely help with recovery and strength. Extra calories generally means extra carbs which will help retain water and add fat fairly easily(most people). Water weight and/or fat equals leverage and more leverage means more weight lifted. Also, I don't know if you have ever had to diet bodybuilding style but if you have...you know that strength will usually go down so in this situation it is just the opposite. Look around on the net...post on a forum with strength coaches. You'll find that most of them carry a few extra pounds above "normal" weight to help keep strength and recovery levels up.
For definitive answers I reccomend elitefts.com Dave Tate or Jim Wendler...those guys are the pinnacle of powerlifting expertise. Justin Harris is the nutrition guy. For a bodybuilding point of view ask around the forums at animalpak.com Whatever you do stay away from the bodybuilding.com forums, you won't find any truth there.