To Arnold maybe, but certainly not to all Terminators proven by the second part of the law: "... as long as such protection does not conflict with the First or Second Laws". Now the first two laws are about protecting humans, which given the name would suggest they were not programmed to do so. 

There is an instance in the latest movie where one of the machines terminated itself. This was when they were testing the magic signal. While it wasn't a "terminator" it came from the same place and therefore had the same programming. The difference with Arine is that he was reprogrammed by the Humans and therefore could have had the three laws apply. 

So I would say terminators are not bound by the third law in any way. 

Does a terminator have a form of self-preservation or prohibition against suicide?
If you summon a creature and give it any item then dismiss it, does the item go with it?
