Doubtful
Over at McSweeney’s, Joshua Tyree on the Implausibility of the Death Star’s Trash Compactor:
5. And what of the creature that lives in the trash compactor? Presumably, the creature survives because the moving walls do not extend all the way to the floor of the room, where the liquid is. After all, if the walls reached the floor, the creature would be killed each time trash is compacted. The design employed on the Death Star must allow the organic trash to filter down to the bottom, where the parasitic worm-creature devours it. But what happens when heavier pieces of non-organic trash fall down there? Would such trash not get wedged under the doors, causing them to malfunction? Do stormtroopers have to confront the creature each time they retrieve pieces of un-compacted trash?
All valid questions.