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Maybe in your soil, but certainly not in mine! I have heavy clay/silt that takes hours of backbreaking work to do anything with.
Here's a bit of animal psychology. Most animals that dig will dig relentlessly if they think they're getting anywhere. I watched a ferret dig through carpet, then padding, and then hit 100 year old oak flooring. Kept going on that oak every day, knowing that eventually he'd make it under the door. Scratched the finish up and started to groove in the grain, but after a year he'd made less than 1/8" of progress.
Thus, a trenched-in fence will just result in deeper holes. Digging the trench will loosen the soil, and unless you compact it again or backfill with rocks, it makes for easier digging along your fenceline.
Yet, as others have mentioned, few animals have the sense to simply back up and find the edge of the apron. Most animals will try to get CLOSER to the goal and commit their effort, not farther.