Apparently not, you can see this prey item retained its shape:
Their mouthparts extend a long way forwards during the bite, so the prey item doesn’t really move that far during the 6ms of the mouth closing. You can see this if you skip frame-by-frame in the video- the frogfish’s head seems to double in length (and engulf the smaller fish) in a single frame, then retracts somewhat more slowly as it swallows it.
