They most certainly would. And I think their best bet would be in either Montana or Colorado, as both had a huge base of Miners were the IWW (which I don't think exists in this ATL?) was very popular and had sway, or possibly Dakota. Wisconsin is likely out - even if the Socialists manage to take Milwaukee (not beyond the question: both the GOP and Dems had horribly corrupt machiens there, and the Socialists were able to position themselves as the party of clean government - and they also extended needed municipal reforms and programs to the Poles and other groups), I don't think they're really going to have a shot at the governorship. Even in OTL, the LaFollette movement was willing to work with them, and did so many times (Phil LaFollette's secretary and bestfriend was a Socialist, for instance - and his death in a car accident really damaged Phil's reelection campaign in '38 - though that was an uphill battle anyway), and this would suck a lot of the wind out of the Socialists getting the governorship. Though there were rural Socialsits who did get elected to the Assembly during the early 20th century. And though I could see them having regional support in Minnesota, I don't see them getting the governorship,
Now Dakota is an interesting situation, because one could argue that Socialists DID gain control of that state in OTL. The Nonpartisan League was founded by a member of the Socialist Party who formed his own organization to focus primarily on the needs of farmers, named Townsley. Their innovation, though, was not NOT run candidates as Socialists - they ran them as Dems in Dem strongholds and Republicans in Republican strong holds. But once the members were elected, they caucused and planned together. The NPL ushered in state Hail Insurance, state grain mills and a state bank, along with a number of other needed reforms. And so, I could see them doing somethign similar in this ATL - they will still be largely Dems, but they will be Social Democrats who move into that party and start dragging it even further to the Left. And in this climate of the Cinco-verse, I could see their organization spreading far father than it did in OTL (In OTL it moved into Minnesota and helped found the Farm-Labor Party and then northwards into Canada where it become important in Manitoba and Sashkatchewan, but was met with violent resistance further South in the American Plains)