There seems to be an issue with closing core overlays when the tab is not focused. The overlay itself is not visible (opacity: 0), but both it and the core-overlay-backdrop still cover the page and prevent page interaction. The problem happens regardless of whether layered is set.
To reproduce, go to the core-overlay demo and open dev tools. In the console, paste:
var overlay = document.querySelector('html /deep/ #overlay');
window.setTimeout(function() { overlay.opened = true; }, 10000);
window.setTimeout(function() { overlay.opened = false; }, 20000);
Then switch tabs. Come back to the tab 20 seconds later and the improperly closed overlay and overlay backdrop block page interaction.