I would say it loads the rear shock a bit, and makes the front kinda float. (Hammer Mode) Hanging off the side has always felt very unnatural to me because you have to 'unglue' yourself from the bike. I hang onto the bike with my ankles and knees, not so easy to do while pointing a knee towards the ground. I point mine at the gas take to hold on. So when I hit a sharp dip, it doesn't bounce me off the seat, I stay planted ready for the next one.Part of me feels it's a monkey see - monkey do sort of thing, where everyone is just copying each other.
I would guess there is a speed/centrifugal force minimum that hanging off the side would have any effect on things, and I would bet that speed is very fast.
Let's take a look first of all at how the throttle can effect the suspension of the bike and then we can get into how BODY Position comes into play.
You said that rolling on the gas "loads the rear shock a bit, and makes the front kinda float. (Hammer Mode)" and ya, that's true to some extent. Hammer mode as you said would be a little bit more aggressive than a smooth throttle roll on, lol but the basics are still the same.
From Twist of the Wrist II "Shocks and forks produce the best road holding/traction mid stroke (in approximately the centre third of total travel). Fully compressed (bottomed) suspension is rough and "topped out" (fully extended suspension similarly lacks good response to road conditions."
Also from Twist II "Good suspension depends on both the hardware (shocks, forks weight on parts) and its position on the bike, (head angle, fork offset, engine location for stability. Throttle control has a huge effect on both."
So your job as a rider is to use throttle control to put the suspension in the correct range. If you don't roll on the gas while cornering and coast (especially during a downhill corner) then the suspension isn't in the correct range because you haven't transferred any of the weight off the front and to the rear....the bike can feel heavy on the front, a bit unstable or worse, can lose traction because it was pushed to carry too much load while cornering. The reverse can also occur, if you corner and give it too much throttle, too much weight goes to the rear, not enough on the front and again suspension isn't in the correct range so the bike doesn't feel as stable or planted as it could. Also, a stable bike will hold a predictable line.
What would the ideal situation be when cornering then? When would you want to roll on the gas and how much in order to get it into the correct suspension range?