so there was a village and a raid and two pet wolves  i did not want them dying as they were low heath so i told them to sit

later i died  and realized that i did not set my spawn so my friend who was helping me pushed my wolves into the water 

expected to happen the wolves teleport to me not invisible at all

what happened

1. the first wolf  was not watched teleport and when arrived was invisible
2. later my wolf fell into my friends moat thing at there house i could see the bubbles my friend came out and as soon as they looked at the wolf in the water he was fixed but not when he saw it on land before that

the second wolf was watched after i told him that the first one was invisible he watched the second one the whole time it did not turn invisible

this is untested on cats or parrots but they  can sit and stand up in water  and teleport to there master so maybe?