The Shulchan Aruch (YD 100:1) seems to draw a distinction between a "בריה" (a whole animal) and "ואבר מן החי" by listing them as separate distinct entities:
"בריה דהיינו כגון נמלה או עוף טמא וגיד הנשה ואבר מן החי וביצה שיש בה אאפרוח וכיוצא בהם"
"A creature (that is, something like an ant or an unkosher bird, or a sciatic nerve, or a limb of a living animal, or an egg with a chick inside, and such things)"
If we extend this inference- ie since the Shulchan Aruch seems to list a "בריה" and "אבר מן החי" as separate entities- perhaps we can suggest that אבר מן החי wouldn't apply to a living creature that was eaten whole.
NOTE: This suggestion presupposes that the SA is referring to a living creature either dead/alive. If the SA is only referring to a dead creature, this line of reasoning may not work.