Sure they can. The pressure difference doesn't mean much to them - they aren't victim to the pressure problems - their lungs can fill with water, and they can equilibrate to the sea-floor pressure without the ill effects felt by humans. And I, at least, would expect zombie flesh to be deadly poisonous, so they wouldn't get eaten by fish quickly.
And zombies are beyond patient, and into relentless. It being really difficult is not a problem for them - they don't give up whining that it is too hard to walk cross the sea floor. They don't run out of air. They don't need food. They don't get tired. They don't have anything better to do with their time. They just keep coming.
"Can't" isn't in the zombie vocabulary. Not that anything is, of course, but "can't" really, really isn't.
Yes, a major sea floor trench will slow them down, but it won't stop them forever - in fact, sea floor trenches are probably a source of new zombie outbreaks. A few find their way in there, and find their way out decades later.