Is it possible to make non-sweet icecream (i.e. with no added sugar or sweeteners)?
Sugar does more than just make ice cream sweet. It also controls the way ice cream freezes. Without it, you tend to get bigger ice crystals, which have an unpleasant mouth feel.

There are substitutes. Breyer's sugar-free ice cream, for example, has guar gum, polydextrose, cellulose gum and gel, and maltodextrin, among other things. Home ice cream makers don't have ready access to all of those ingredients, but there are recipes for making sugar-free ice cream at home. (I haven't tried them and can't vouch for them.)

As for making savory ice cream... yeah, people have tried. Most of those are nonetheless somewhat sweet. That may be in part because coldness really dampens flavors; people enjoy melted ice cream because it's even sweeter than cold ice cream. Umami flavors are hard enough to do well even warm, and they'll become very bland when frozen. Maybe if somebody wanted to really pack an ice cream with marmite and Parmesan cheese...