I doubt that can be done. Strawberries spread by stolons (runners). As the strawberry plant runners are sent out, the nodes will develop the adventitious (its own separate roots) roots, send them downward, and establish the new clone plant once contact with soil is made. Once established, the intermodal runners will dry, shrivel, turn brown, and eventually separate leaving two independent plants: the original and the clone. This allows them to find better soil or areas of better sunlight.

I don't see how the stolons are going to survive without soil.