If the VS departed during flight, then, and I'm theorizing, it presumably would have been nearer the LKP, and immediately buoyant on the ocean surface. The French overflew the LKP and areas west and east of the LKP (perhaps as much as 10 NM west) at about 1530 hours on June 1, and saw nothing. The Brazilian AF also overflew the LKP on June 1, although their search box was not as far to the west as that done by the French Dassault Atlantique 2. (Have not found times for the Brazilian search.) Brazil saw nothing either.
The question to be answered is why nothing was seen on June 1, but perhaps part of the answer involves the law of buoyancy, and whether objects detached from a relatively intact airplane as it was sinking, and gradually made their way to the surface.