I was trying to replicate MC-133342, and then one of the ender pearls disappeared after touching the nether portal. I started recording and managed to do it multiple times. I went through the nether portal afterward, and I didn't take damage.
I then decided to take another video, but with my other account in the nether. I discovered that the ender pearl went through the portal, but didn't teleport me.
I have my f3 screen pulled up, so you can create the world using the seed, and recreate it easily. You don't seem to need to be looking at an exact angle, however.