Mikey
Most claimants who go to appeal, will produce additional evidence, should the question be asked at a hearing, which I doubt, your not being able to produce it in time for the assessment would be a reasonable reason.
That said, we would encourage all claimants to try and collect as much evidence as possible for the initial assessment, remember you can still take documents with you on the day of the assessment. If you do this, then you should also send copies to the DWP, see
Sending Documents to the DWP or ATOS With regard the question "do you want to work?", the only advice I can offer, is to be honest, but if your condition(s) restrict your ability, then explain why this is the case.
Gordon