Having just downloaded the free core rules from GW for the new AoS these are the rules concerning your question. No where is it mentioned what type or shape of base it should be or even that it has to be plastic. However all models used to illustrate are on round plastic bases.
1.2 MODELS The Citadel Miniatures that make up your army are referred to as models. Most models have a plastic base that allows them to be stood on the battlefield and that are used when measuring distances to or from the model (see 1.5.1). The base is considered to be part of the model for rules purposes. A model cannot be set up or end a move on top of another model, either wholly or partially
1.3.3 UNIT COHERENCY Units must be set up and finish every move as a single coherent group. A unit with 2 to 5 models is coherent if each model in the unit is within 1" horizontally and 6" vertically of at least 1 other model in the unit. A unit with more than 5 models is coherent if each model in the unit is within 1" horizontally and 6" vertically of at least 2 other models in the unit. If a friendly unit is not coherent at the end of a turn or after you set it up, you must remove models in the unit from play, one at a time, until it is coherent
1.5.1 MEASURING DISTANCES Distances in Warhammer Age of Sigmar are measured in inches ("). The distance between two models is measured between the closest points on the bases of the models. If a model does not have a base, measure to and from the closest point on the model instead. You can measure distances whenever you wish.
So in theory I would say you can.