If you deviate from the route, but notify ATC, there should be a record at the ATC unit and SAR will be able to follow the notified change.
The only record is likely to be the RT recording. Imagine someone filing a FPL from an airfield on the south coast of the UK to somewhere 'up north'. En-route he talks to airfield A for a crossing clearance of their Class D zone. Airfield A would not know he is on a FPL, the pilot's call for CAS crossing is an abbreviated FPL and all that is needed to obtain crossing clearance.
If the pilot then says "I'm changing my filed route to . . . ." what does airfield A do with the information? He may write it down on the strip, although I doubt all would, but nothing would get sent to the centre or destination.
Then, if the aircraft fails to arrive at its destination and people start to look, someone may ring airfield A and ask if they worked it and someone may remember the pilot mentioning a change of route, or see it on the strip. But then there could have been a controller change. Or airfield A could be closed. The route change would be on the RT tape but it takes time to have it played back.
I am not trying to dissuade anyone from filing a FPL, but certainly within the UK, it is only of real relevance to your destination.
VA