Yes the AAIB will search for his Log Book to determine experience. Unfortunately some Log Books are not found or the pilot has not filled it in for some time ( often years). In those cases the AAIB look for other ways to calculate experience ( employers records for instance) or sometimes they have to say in the final report ...unknown. Another good source is the pilots medical renewal forms which require hours to be filled in.
Licences have to be carried so are often lost in the accident. However holders of an AOC are required to keep records so the data is available. For
Private Pilots all that was required for revalidation in the past was a signature in the licence, but nowadays returns are required by the CAA.
Documents which are required to be carried are also sometimes lost, e.g C of A, C of R etc. However, all this data is held by the CAA/FAA and maintenance organisations, so can be easily retrieved.