If the extintion thing will happen fast, there will be just a few artificial objects outside Earth's gravity. Vast majority of satelites will be burned in the atmosphere by then. But we may indeed have left enough objects near geostationary orbits - and that would be a convincing indication of intelligence.

One funny possibility is that we would leave enough evidence to suspect existence of our civilisation of this level, but not enough to establish it up to scientific certainty. We can imagine a bunch of rather gifted allien enthusiasts of Terrestial civilisation being derided by their scientific "establishment" :-)))

Intelligence detection is an interesting problem for science. Positive confirmation by single artifacts looks more feasible than falsification of the hypothesis by single observations. What would Popper say?