Sure, why not? (And just try getting a definition of “living” out of an evolutionary biologist.)
One thing, though–this means that your VNM may not “work” for very long in the sense of doing what it was designed to do. (How long depends on your error-checking procedures.) Thus, if you have two Saberhagen Berserkers, both of which are programmed to a) reproduce and b) kill everything living, and one of them says “Screw killing all living things. I’m just gonna reproduce” (or rather, one of them has a manufacturing defect such that it’s “kill everything living” directive has been deleted), then the “Berserker” which doesn’t waste a lot of valuable time and resources killing all living things will have lots more time and resources to reproduce itself. Pretty soon, you’ll have lots more of the variety 2 “Berserkers” than you have of the original Berserkers which do what they were actually designed to do.
This is definitely something to think about when contemplating nanotechnology and all those neat ideas like injecting yourself with self-reproducing nano-robots to clean the plaque out of your arteries and help your immune system fight off infections.