Would it make sense for me to say "the supposed winner of the world series, the Yankees, played well."

According to your inane logic, supposed is correct because the Yankees could have lost. Of course they didn't lose, so the word supposed should not have been used (unless you feel they actually lost)

In the same manner, the colonialists were patriots, not supposed patriots because they won.

However, I'm sure your buddies on the left fringe agree with your use of the word supposed.