Ocean and tidal currents are not modelled in SHIII so you can't "let the current pull you through", but you can run at slow or 1 or 2kt to sort of simulate this action but you have to actually push you boat everywhere.
Almost all ships do "drift" at around 0.5kt or less when they are stationary but it's too slow to really notice unless you sit a watch for a loooong time.
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