No, Hades = the Grave.
Or realm of the dead, whatever.
The place of 'eternal punishment' in the NT is gehenna. As most people are thinking of that concept when they hear 'hell,' in most minds Hell = Gehenna. Unfortunately, the Most English translations render both Hades and gehenna (and tartarus in some) as 'hell' which is most unhelpful.
Zag: Paul never mentions gehenna and that's a clue? What about Jesus, did he ever mention gehenna?

Isn't that a bigger clue?
Besides, it isn't like Paul was shy about the concept. Romans 2 seems to be clear enough. For eg,
"To those who by persistence in doing good seek glory, honor, and immortality, he will give eternal life. But for those who are self-seeking and who reject the truth and follow evil, there will be wrath and anger."
Wrath and anger sounds a lot like gehenna to me.

Notice how it is paired up with 'eternal life.' The parallel seems justified... the first half gets eternal life, the second half gets eternal wrath. Anyway, I don't think you can say that Paul never talks about such things.