Possible, yes. I think top to bottom we have a better roster than Nashville. I believe they were the best team in the Cup final this year. I think if it's possible for them it's possible for us.
Next season Forsberg, Johansen, Subban, and Josi are better than any player on the Wild. Ellis or Ekholm would likely be number two defensemen on the Wild. Kevin Fiala would be a top-six guy on the Wild. Arvidsson I don't believe to be a total fluke any more than Granlund's breakout was. So I think their top talent beats the Wild's (strong group of prospects too).
Depthwise, the Wild might be better - that remains to be seen. The Preds lost their Koivu when Fisher retired (Koivu is better too). Both teams lost an important scoring winger in Neal and Pommer and good depth in Colin Wilson and Erik Haula. Adding Cullen made the Wild's fourth line into an asset yet the Preds added Nick Bonino, who is no world-beater but did play in front of Cullen for the Pens last year.
As Wabit pointed out, the Wild's major weakness right now is backup goalie. Saros looks really good (.923 save percentage in 21 games last season) though Stalock has more experience overall.
I feel safe saying this is a top-tier squad that should be in the playoffs. Nashville will be a team they have to beat consistently, same with improved squads like Edmonton, Calgary, LA and Dallas.
Not sure what the core of this team is but I can see them having success in the playoffs without Parise, not so much without Suter, Koivu or Dubnyk.