I wouldn't think so as you're not planning to sleep in there so cutting out light is less important. But the curtain material might fade on the reverse if it's unlined whereas the lining protects it.
Occurred to me that if you already have shutters, assuming they work, are curtains essential? We have no curtains at the back of the house downstairs as we're not overlooked and have never missed them. One less thing to collect dust.