When zombie pigmen were pursuing me in the Nether and I went through a Nether portal (no teleporting, just walking through), the pigmen became trapped in the portal and despawned from the Nether, as if they traveled to the other portal. When I traveled through the portal, the pigmen were not there. I'm not sure if they just did not respawn on the other side because there were no players around, or if there is a problem with teleporting mobs.

I recorded a demonstration and posted it here: https://www.youtube.com/watch?v=HSLVXv0EllU