Well, I did several teleports from sim to sim around the Beta grid while wearing a very complex furry avatar, and so far I haven't had any of my attachments fall off at a result of a teleport. I'll try that some more soon, but so far, so good.
On the other paw, after one TP while still in my low-lag Human form, I was told that my face was the infamous "missing texture". Looked fine to me, and checking my appearance and then rebaking did resolve it rapidly.