Nit-pick: more exit pupil than sensor size, but they're a rough approximation anyhow.
But you're correct that the short (actual, not equivalent) focal length of camera phones makes an f/1.8 completely irrelevant.
Sensor size doesn't really have an effect - it's about focal length. The reason sensor size seems to have an effect is because for the same field of view with a bigger sensor, you have a longer focal length. For the same focal length, aperture and focus distance, a larger sensor doesn't change DOF; it just adds more of the surroundings to the outside of the picture.
So on a full frame sensor camera, shooting someone's portrait with an 80mm will give you very shallow DoF, on a sensor the size of an iPhone, it's probably close to infinite.
Edit: I don't think the above is technically exactly correct...Here's a good explanation: http://www.cambridgeincolour.com/tutorials/depth-of-field.ht...