No, I dont think they do. At least, certainly not in the same sense as cats and dogs. Llamas are herding animals. They have evolved as grazers and browsers and, whilst they have worked with Man for thousands of years in the Andes, their dependency on the latter has never developed.
But dont get me wrong: I love my llamas, but I have accepted that, unlike my cats, the relationship is one-sided. I cannot have a meaningful relationship with them. I very much doubt that I can actually give to them anything that they value ....apart from food.
Llamas do not really enjoy being touched ( the parent never touches the young cria) though many will tolerate it. In general they prefer to be left with their mates in their field, which is what Nature intended.
I recently read an article in a 1990 back copy of an American magazine called "Llamas". It was a description of how one man, Peter Illyn, and two male llamas had travelled a thousand miles on a packing adventure over several weeks in the Cascade Mts of western USA. I have contacted Rev.Illyn, (more than two decades after he wrote his article !), and it is with his permission, that I can give an extract from his story:
I think that Peter Illyn has been both honest and realistic in the above. Whilst I wouldn't be without my llamas, particularly the boys, my experience of their ability to return affection has been much the same as his.