Not being ATC qualified, I'm not in a position to make a definitive judgement on that but I think it makes sense to do whatever one can to look out for one's own safety. Obviously, if flying VFR you may choose not to get, or be unable to get in-flight following. I've had this happen a few times in the north west of UK.
The "responsible person", if not of an aviation background, should be briefed on what action to take if you become overdue. In reality, this would possibly "kick-start" the system into action more quickly. If you had also submitted an accurate, written flight plan, it would be retrieved and the route you took is then quickly available to the SAR system.
Interesting. In a nutshell, then, could this be summarised by saying that the VFR Flight Plan would be used re-actively rather than pro-actively in the case of an emergency / triggering-SAR response ? (pending ATC-qualified comment). If so, then the answer to my original question seems to be along the lines of a VFR Flight Plan has some value when it comes to assisting with the emergency response (after it has been triggered somehow), but other preparatory actions may be even more valuable (e.g., informing a "responsible person" who can pro-actively trigger the response).