It is very difficult to answer a question like this in an objective way because much of Turner's thesis had to do with his interpretation of what impact the frontier had on the American character.
Many people today disagree with Turner's thesis. It seems old-fashioned to them with its emphasis on the idea that the settling of the West was a positive process that improved the country. Modern historians are more likely to want to look at the ways in which the frontier impacted Native Americans and women and Hispanics as a way of making our view of the frontier more nuanced. It is hard to prove that modern ways of looking at the frontier are better or worse than Turner's, just that they are different and show the impact of changes in the way we think about things like race relations.
One thing that we might think about is whether we have actually lost the characteristics that Turner gave the frontier credit for. Have we really become less democratic and less self-reliant? If you would say we have (and again, this is opinion) then you might conclude that Turner was right.