The monster description (and the monster tile) for shadow trolls seem pretty straightforward in telling they are corporeal and are more or less troll zombies. If zombies have pockets I don't see why shadow trolls shouldn't.
Shadow centipedes seem to be corporeal as well (but those of course shouldn't have pockets due to other reasons).
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Unlike its living brethren, this troll's skin is a sickly greenish-gray color, it has no hair whatsoever, and it smells downright awful. It mumbles as it walks, but it sounds more like vomiting than speech.