Iain
PIP is not a work-related benefit, many PIP claimants work, some with the highest award, so your PIP award does not mean that you are considered unfit for work.
It's very unlikely that the assessor will be sent a copy of your PIP Decision and the associated report, they have no direct access to it, a DWP Decision Maker may but there is no guarantee that they will refer to it.
If you want your PIP award to be considered in regard your limitations then you need to include it as part of your evidence, you will need to explain why it is relevant to your ESA claim, although some of the criteria do overlap, even where it does the actual criteria is different.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems