Does time pass in the game when I'm not playing?

No it does not.

It stops as soon as you leave the game and starts as soon as you join the game again.

Perhaps this has changed in recent versions of Minecraft PE, but I think time does continue while the app is inactive, at least in some form. I just tested by harvesting a Sugar Cane field and switching away from the app. About four hours later, I switched back to the app to find that my field had regrown and was ready for harvest again.

One thing to note: most of the Sugar Cane plants had only grown from one block to two blocks during the four hours my Minecraft PE app was inactive. My gut tells me that with four hours of non-stop playing time the plants would have all grown to their full three-block height. So perhaps time still runs while the app is inactive, just slower?

Edit: I'm playing Minecraft PE on my Android Nexus 6.

Edit: Just ran another test. I started a new world, left my character standing in an open field, and switched out of the app. The next morning, I opened the app to find my character had died: