Would they? I remember back to the 2011 draft when Burns was traded and you heard cheers at the announcement. I'm going to guess that none of those people were cheering because Burns was leaving, they were cheering because changes were being made. How many of those people do you think were season ticket holders?
If they go into a multi-year rebuild where the team is terrible then yeah, ticket sales will suffer. But I don't think they're anywhere close to that. Selling a player or two at the deadline and giving up on a year where we've already lost Dumba and Koivu doesn't seem like something that anyone will actually get mad about. Considering how the last few years have gone the reaction would probably be the opposite.
While fair, most were lauding at the Burns trade because they were seeing known-scorers coming back in a trade-trade deal that sent a diva in Havlat and a player in Burns for Heatley/Setoguchi who were coming off decent years with San Jose. At that time, the Wild literally had no one who could score a goal in their forwards. I mean that was when Brunette-Koivu-Mittens were the TOP LINE. And I think that was the year the Wild's only All-Star was a rookie for the rookie game and not even the actual all-star game.
Here is the concern I see with the second half of your comment. People will be irate no matter what you do, right? Believers in the team (or homers at least) are going to lose their minds if they trade Spurgeon or Granlund. From the perspective of blue-blood Wild fans it will be the tell-tale sign that they've given up on the season and probably will not get anything back that is remotely close to what they believe the Wild should get. For example, if they trade Spurgeon to say Toronto for a 2019 1st rounder and a prospect -- there is no tangible way that most fans will see that as a win/win. The Wild lose a star Dman and the pick will be in the last 20's and the prospect will probably never pan out to what the status quo would be for that type of trade. Rubes will be upset because that signifies the team is going to suck for a long time. What I think gets lost on those who live in Duluth/Twin Cities, is that the rest of the state doesn't care about hockey nearly as much as we all think our state does. Hell, even in the metro about the only way you'll get the sound turned on in a bar is if the Wild are in the playoffs. Once the team is in the bottom of the standings you most likely are not going to see many tuning in. TV contracts aside, it isn't good for promoting the game and getting merchandise and the rest out to more than just those who live in the 763/612/651/952/218 area codes.
However, in that light -- the likes of Spurgeon or even like Brodin would be considered probably moot to most fans. It is the "one of us" mentality that seems to drive this state batty when it comes to hockey players. A player like Zucker or even Staal are largely seen as adopted Minnesotans in my opinion. Zucker because of his wife and community driven activities. Probably Staal because I'm sure Edina HS is just salivating at the thought of his kids playing hockey there if he stays here, which in turns drives many who idolize the HS State Tourney to pressure him to stay for that very reason. Just an observation, not a fact nor am I saying it is fact or truth.