Check out this video of an American speaking excellent Spanish, and I mean excellent. His name is Richard Vaughan, of the Vaughan language schools in Spain. (He should plug LingQ for me since I am plugging Vaughan, but then I was just so impressed with his Spanish.-:)
Would his Spanish be more impressive if he sounded just like a native? I don’t think so. He has total mastery. This is the ultimate goal of language learning. Pursuing the goal of actually sounding like a native is unnecessary, a distraction from the real task of language learning, and highly unlikely to succeed. I have seen people pursue this goal and end up sounding like caricatures, while not achieving the language mastery that Vaughan has achieved. Here is a video I just did on the subject.