Not likely. He seems to be drawing the distinction between an earthly death and a second, permanent death. When you view that passage in light of Revelation where the damned are cast into a lake of fire and destroyed, it makes more sense to interpret the passage that way.
It's also worth noting that Paul's epistles and the synoptic gospels present a much different view of the afterlife, as bodily resurrection at the end of the age is emphasized over the idea that people go to heaven or hell after dying. The Jews certainly didn't believe people went right to heaven or hell after death, so it seems pretty reasonable to conclude Jesus, a Jew, also promoted that idea.
