You wouldnt have thought so. But I would expect if cctv saw him going up there then it was checked later on and no sign of him coming back so in that case we can assume he continued either up the mountain or tracked the more coastal route towards the only signs of life nearby, Agia Marina, though theres no sightings of him going there.
That BBC clip implies he was intending to loop round the peninusla to get back to Symi, but why would anyone sane walk 2 miles in the wrong direction, to then have to walk say 3 miles back to get to where you're going, up a mountain, in 40 degree heat, peak daytime, armed with nothing more than a brolly. Doesnt make any sense and even if it did, where on earth is he. 12 hours or so of multiple search teams, dogs, helicopter, drones and no sight.