I store my Studio shutters closed usually, if only so the lever doesn't stick out, but if I remember correctly (and I may not, because I haven't opened one too recently) there are two springs in a Studio shutter--one engaged in the open position and one in the closed position--so I don't think it really matters.
Followup: There are two opposing springs for opened and closed. (Easiest CLA ever too) So I guess I'll store mine closed and use the cable release. Thanks guys!