Yes, taking out the Pirates is the most efficient way to protect your trade fleets. Plus, there's a good chance you'll capture a Galleon or two you can replenish and use yourself.
Be aware, though, that the Pirates of the Caribbean will re-spawn (but without Captain Jack Sparrow) at Curaçao if the Dutch are destroyed.
The Barbary States are easy enough to capture, but hard to hold. Being 100% Islamic, they tend to escalate into full Rebellion quickly. This ties down land forces better used elsewhere. It's probably better to neutralize them by defeating their fleets and allowing other Mediterranean factions to blockade their ports.
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