When an overlay ad is displayed, the container should be made visible and I can see this is attempted through the following style rule:
.oo-player-skin-plugins.oo-overlay-showing:not(:empty) { display: block; }
This is assigned when the overlay is showing and the container is 'not empty'. However, an additional line to update the z-index is also needed, as otherwise the container is obscured by the div with classes "oo-state-screen" and "oo-start-screen".
Please see the following PR for the suggested change: https://github.com/ooyala/html5-skin/pull/768/files
Example NonLinear Overlay test page: https://featured.dugout.com/preroll-test/coull.html