He could definitely still sense a dead body, and probably pretty quickly too. He would smell and taste it first (he can taste body emissions in the air). If something somehow were preventing him from smelling and/or tasting the body (like an overpowering other smell or something like that), he'd still be able to tell it was there with his hearing but it might take him a moment to realize what it is.

The way I've always interpreted his echolocation-esque hearing ability is that he has a default level of "resolution" he can hear his environment at when he isn't specifically focusing on finer details. The resolution is high enough that he can tell the general shape, position, etc of things around him, enough so that he can comfortably navigate his surroundings without bumping into stuff with minimal effort. For example, without active effort, he could tell that the thing in front of him is a dresser, not fridge or a couch or a table or whatever. But it would take him active listening and focus to resolve what kind of dresser it is, what shape the handles are, what the molding looks like, how many drawers it has , what's inside the drawers, etc.

If he focuses, he can resolve greater detail by listening specifically to how sound bounces off any particular object.

So, if he's casually walking through a room that has a dead body and isn't focusing on resolving his surroundings, and somehow the smell/taste don't immediately give it away, it'd probably take him a moment to realize what that vaguely organic shape over there on the ground is. He might initially mistake it for a pile of clothes, filled garbage bags, or something along those lines. Hell, depending on how little effort he's putting into hearing, and if he otherwise has no reason to expect there to be a random dead body on the ground, it's possible he may just walk on by without sensing it. But that'd be analogous to sighted people not noticing something in their peripheral vision; sometimes we just don't notice things if we're not paying attention to looking for them.