Old Crock
Any revised Decision that the DWP might make, with or without a new assessment will apply from the date of the original one.
A second failed assessment will reinforce the DWP's case that you not qualify for an award but this is not necessarily fatal to your appeal, their reasons may be the same as the first assessor and just as invalid.
Based on what we have seen in the forum, recording an assessment is unlikely to make any difference to the quality of the report that is produced but it is still worth doing if only to have an accurate record of what happened.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems