OK, speaking from experience, which I will relate below, I will always have the FEL attached and don't hesitate to put stuff in it that I need to relocate.
Was planting native grass seeds on a dirt tank, going up and down the slope (not sideways) and turning around on the top of the tank to head back down. FEL inches off the ground(maybe 3 inches), loaded with about 300 lbs of rock.
A moment of inattention and I found myself doing a U turn a moment too late on the top of the dirt tank.... right front wheel went just a tad further down the opposite slope than on previous turns and in a flash the left rear loaded wheel was off the ground. I dropped the FEL further and stopped to survey the situation.
Turns out that the FEL was dug into the ground (the round part, not the teeth) and because of this it actually PREVENTED my rolling over. It provided a point of ground contact further in front of the tractor than the front wheel and with some DOWN FORCE. Thus, it PREVENTED the rear wheel from rising further, thus dramatically raising the COG and preventing allowing/initiating roll over.
Think about it.. for a rear wheel to rise, the tractor footprint rectangle must dip down on the opposing corner. A FEL out there extends that rectangle footprint beyond the front wheel. If close to the ground and dropped/driven into the ground when a roll starts, then it MUST assist in preventing the further rear tire elevation.
I was in 4wd low range, thus going very slow and momentum was not an issue, just balance.
I got out of it by strapping the tractor to my F350 to prevent actual roll over, getting additional help (my son), then SLOWLY turning front wheels downhill while AT THE SAME TIME keeping FEL in strong ground contact with hydraulic down force to maintain some modicum of stability. Ground was loose, thus slid under the FEL just enough...didn't "catch"....I also left the Brillion grass seeder pin hitch attached to the tractor...providing backdrag and some down force on the tow hitch.
Net, my experience leads me to conclude that in my case, with my tractor, in this instance, with me driving and taking the actions described, THE FEL PREVENTED A ROLL OVER.
I will tell you that I had to struggle mightily to dismount the tractor on the uphill side when the tractor was stopped. I have a cab. I truly don't believe there is any way I could have bailed out uphill from a moving non cab tractor. I would consider that move to be a suicide mission in the case I described.
Yes, my experience goes counter to what many have posted here. All I can tell you is that in my case, I WOULD have rolled over except for the FEL and the way I applied it when things went downhill (literally) very fast! Trust me, you DON'T have 1 to 2 actual seconds to take action. True time frame is about .5 second.
With my first hand experience, I will continue to keep FEL on and extremely low whenever I am on uncertain ground. You may decide that you wish to take a different approach.
Stay safe out there!