No, they don't. That was the big issue last year, but they largely rectified that matter. Even Buxton's K% is under 30% now. As a team, the Twins are tenth in the league in strikeouts this year averaging a very good 21.1%.
Presuming their power evened it out, I figured the team could afford two regulars who whiffed over 30%, maybe three if they were spaced out in the lineup. With Julien off the roster, they only have one such player. It would be great if Wallner could reign in the strikeouts a bit more, but at this time, it's not a problem, so rip away big guy.