How long would this take in this search?
Agreed. Chemical analysis would not be practical.
I envisage a slick of dye emerging on the surface downstream of the wreckage on the seabed, which in clear weather would be visible to a wide-area search more quickly than pieces of floating debris. It only needs to be there long enough for the first search plane on the scene to record the GPS coordinates of the start and end of the slick, allowing a pretty good extrapolation to the seabed location.
I don't pretend for a moment that this would be foolproof, but it could be a valuable extra pointer to the location of the FDR.