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:

....... The
llamas were hard workers and good companions, but they never gave me any unsolicited
affection.  I longed for a surprise muzzle and hoped that the constant interaction
between us would allow a bond of mutual affection and trust to develop. The
llamas, however, never seemed interested; if I walked towards them, they would
get up and walk to the end of their tether, trying to avoid contact.  Although
they stood still for my loving, they never initiated it.  The best I got from
the llamas was a feeling of quiet toleration.  At the end of the trip, I released
the llamas in their field for the first time after being tied to me for the
entire summer.  After five seconds, I walked towards them to see if I could
catch them, but they gave a snort and ran away. They are now exceptionally
well-trained llamas, but no more loving than before the trip! 

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.