Mobs can spawn on shulker boxes

Confirmed. This can be easily tested by creating a new superflat world with the following preset:

minecraft:bedrock,2*minecraft:dirt,minecraft:shulker_box;minecraft:plains

Slimes spawn everywhere, and at night time, normal monsters spawn on the shulker boxes as well.

This relates to MC-155545, which also demonstrates that shulker boxes are now essentially solid blocks in 1.14. They conduct redstone power, and can prevent chests opening.