Did Charles Sturt achieve the main aim of his journey?

It depends on which journey is meant.

Charles Sturt's early expeditions were very successful. He discovered and named the Darling River. He also discovered where the inland rivers flowed, as the Lachlan River flowed into the Murrumbidgee River and the Murrumbidgee flowed into the Murray, which then was found to empty into the Southern Ocean. This discovery opened up much of inland New South Wales for settlement, and also led to the colonisation of South Australia.

However, Sturt was certain there must be an inland sea, and he explored through the inland deserts in an attempt to find it. He failed to find the object of his search, as no inland sea exists, but he helped map more of Australia's interior.