Great idea but no. There is no system on-board that records the meta, ephemeral or indeed any type of underlying data. The US are nuts when it comes to locking-down everything with crypto and anti-tamper systems - everything on F-35 sits in a walled garden. The only exception is for trials where a crate is carried in the righthand bay but everything remains locked down and the system does not work normally with the crate sucking point-to-point data from the fibre.
The US have worked very hard and spent lots of money to ensure no nation has the ability to do the stuff that we would really like to do with the jet. On the plus side, should one be left in an unfriendly state the capability is not compromised.
That seems to be a definite missed trick in that case. That is a shame. I would have thought that would be an extremely useful capability to have (not to mention, groan, yet more money to fork over for the workstations and other associated tat) and as a foot in the door for other systems that do similar stuff.