No.
It doesn't say so in the Bible plus the fact that God promised Adam & Eve that they would die the day they ate from the tree - and they didn't physically die, suggests only two possibilities:
a) God lied and the serpent was telling the truth.
b) He was talking of a different kind of death (which I understand to be spiritual), a theory which JWs discount by doing mental gymnastics with the time scale!
The big problem for JWs (and a lot of other Christians too) as far as I can see is that they believe everything was created perfect - and physical death just doesn't fit into that category. The reality is that God created everything very good - ie just as it should be, along with the laws of nature, weather systems, earthquakes, viruses etc, and death - He created a complete natural order which is in a sense, 'perfectly flawed'.
That is a massive difference and hard to grasp if you can't imagine a perfect God creating something in a seemingly imperfect manner.