I think the only honest answer to your question is that outside the UK, then almost certainly, but inside the UK "it depends".
I suspect the "it depends" depends a lot on the airport that you are going to. If it's got full ATC, it's more likely SAR will be activated, but still no guarantee.
Also be aware that flight plans don't always work. A number of times I've arrived back across the Irish Sea, which flight plans filed, and left from a controlled airport, only for Dublin ATC to tell me on initial contact that they've no flight plan for me. (And presumably no departure message either). So in those cases even though SAR is supposed to be activted in Ireland for a non closed flight plan, nothing would have happened.