If a chest cannot be opened because it is blocked from above, it will not accept items from hoppers.

Construction method for test is illustrated in 2014-05-22_19.47.36.png
Items shown as not moving out of hopper in 2014-05-22_19.47.27.png

Items will move from hopper to chest with slabs or stairs above chest, but not any full block, including a double slab.