I wouldn't see why not. I've got 3 kinds of allium growing in Nebraska-Christophii, Alfuensa and Nigrum. I've seen them grow with vigor in downtown Chicago and it's not warm and sunny there, either. Especially if it's in a sunny spot. I haven't grown Globemaster myself...but someday. Heidi

Kinda depends on what part of Minneapolis, when dealing with borderline zone 4/zone 5 plants. Some microclimates here are far milder than others.

There is a significant hardiness divide between zone 4 and zone 5 plants that has to be allowed for. But there is also a drainage issue especially for alliums. Also if you get northern adapted stock rather than southern adapted stock you are also more likely to be successful with borderline species and varieties.

In short my answer to you is a definite maybe. Sorry we sit on a cusp here, but in a few years with the way climate change has been going, that will have moved north of us and then there won't be a question. Already some true zone 5 perennials and woody plants are proving to be suitable here, while others still are not quite. I say go ahead and experiment. With a bit of forethought and planning you will probably be ok.