No,
While hell is the consequence of sin, it is only because sin is the means by which one expresses their choice to go to hell. Given that this is a bad choice to make, one could say hell is a punishment. But only so far as it is a consequence for a bad decision.
The threat of hell does not come from God . . .
The threat of hell comes from rejecting good deeds and do vile deeds.
Hell as a consequence of sin rather than the punishment for sin
Just as jail is a consequence for crimes or criminal activties.
God is an observer. Everything that we experience is by our own choosing(Hell or Heaven).
God judges us all(Atheists or Theists), solely based on our deeds(Good or evil), while alive on earth.
Hell is a place of punishment and people are punished because they've done wrong.. In other words, the only reason people go to hell is because they've broken God's law.

