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.
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[media][media]

Works as intended. See MC-7543