Interesting: here's my thoughts, but look to one of the moderators to correct or confirm.
Try attaching something to line that when lowered into the water will give a strong return signal. Next, with no forward motion but rocking, lower it to be near but we'll separated from the bottom. If as the boat rocks, the return from the lowered item stays in the same place on the screen, then the 'fish' returns are being stabilized. If the 'fish' return moves sideways on the screen in accordance with the boat rocking then stabilization isn't taking place.
Another test, done simply just looking at the bottom signal in a big swell - does the bottom move up and down or is the 'heave' being stabilized?
In any event, the display is a real time image - no history is shown/maintained. It's a fleeting glimpse of what is under the boat at the immediate moment. It's a wide side-to-side and narrow bow-to-stern view under the boat, that when watching it gives a real time sense of how deep and off to the side of the boat something might be.
It's an improvement on the old/original 'A' scope in that you get information on which side of the boat something is.
Personally, I think your question, and the result of the above tests are interesting. As a practical matter though, I wonder: would stabilization have significant value? When, how, why, who finds that display to be the best - in particular, when/why is it preferred over the triple beam display?