The answers depends a lot on "what kind of vampire". We could make, for example, one distinction here:
a) The, let's call it, "pseudo-realistic vampire", with some (pseudo-)biological reasoning for the whole vampire mess (a virus, whatever). Such a vampire would have a (pseudo-)biological reason for needing blood - and a synthetic blood could be good enough for them. Of course, such a vampire could need blood for purely psychological reasons, in which case it depends on those reasons if synthetic blood is good enough.
b) The "mystical" vampire that draws from the "life essence" of a person with blood only being the carrier or even just a symbol for that. Such a vampire would probably not gain much from synthetic blood, since it has no connection to an actual living being.
But of course, there are many more possible variants of vampire and depending on your choice of vampire "style" the answer varies. Some might live from synthetic blood and even prefer it (how many people would want to suck milk from a living cow if the can have it delivered to their doorstep in a clean bottle?), for others synthetic blood is just something that looks like blood but doesn't actually nourish them.