If you get into the Skyclub in Minneapolis, it'll be because you're a Gold Medallion international passenger "flying in any cabin."
Complimentary access to most worldwide SkyTeam lounges is available to Diamond, Platinum, and Gold Medallion Members when traveling in any cabin on a same-day international SkyTeam-operated flight. Members must present membership card and their same-day ticket for an international SkyTeam-operated flight or same-day domestic SkyTeam-operated flight connecting to an international SkyTeam-operated flight for SkyTeam lounge access. SkyTeam lounge benefits are provided only at the departure airport and not at the arrival airport unless connecting to a qualifying SkyTeam flight. One guest allowed.
I had no idea that VS wasn't actually on the official list of Skyteam partners. I mean, they seem to function as partners in every possible way. I suspect the club staff probably assume that they are Skyteam and will let you in at MSP based on the above GM benefit.