The question is basically the title. Is it possible to do so through NTS, or directly through SVN?
I can't comment on SVN but if they have an API, it should be possible. As to the NTS, there is no API but it is just a website, you might be able to do this with a Neoload test, you could even you the test as code functionality
As you noticed, NTS relies on Subversion (SVN) over HTTP so you should be able to use any SVN client that handles SVN over HTTP to download your project.
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