To first answer a broader question, we have had a number of members reporting backdating of their award to the Review date where it has been clear that they met the higher criteria at the time they completed their form.
As to your specific question, if there is a deterioration while the claimant is waiting for assessment that would change any likely award then they should report it the DWP. I would recommend that their letter follows the format of the PIP2 and explains the changes for each Activity.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems