My honest expectation is something similar to what happened last year: giving an opponent just about everything that it can handle, but it not being quite enough to advance. This could be the year that they play their first Game 7, but, while pushing it to Game 7 would be a mark of improvement over most previous years (when they lost in 5 or 6 games), not having played one before and doing so on the road isn't a recipe for success.
What worries me is their mental game... the ability to step it up when things are on the line (look, for example, at how they've failed three times now to clinch a playoff spot) and that confidence when things aren't going your way that stops things from snowballing out of control. My concern is that they're similar to the Blues and Sharks, two teams that tend to enter the playoffs with so much momentum and confidence (similar to the Preds right now), only to stumble in the playoffs largely because they don't know how to respond when their opponent systematically picks apart their game as a series goes on. Maintaining confidence when things are going well (i.e. during a hot run) is very different than maintaining it when things aren't going well, which is a priceless skill in the playoffs.
I'm not writing off an upset and an advancement to Round 2. If I were to assign percentages, I might give it a 33% chance. It's a decent possibility, but I can't honestly say that I "expect" it or think that it's the likelier outcome, because the West is so good this year and their opponent will have the edge of home ice advantage (which, as I mentioned, could really come into play in a Game 7).