I saw the production as well -- during its out-of-town tryout. I was expecting a kind of traditional "big" R&H show, which No Strings certainly is not. I remember Carroll as gracefully beautiful who wore lots of stylish -- for the times -- dresses. Otherwise, the show itself is rather thin, both musically and dramatically, with most of the tension coming from the unstated racial dynamic, which at the time was wildly dramatic. But there is a reason that I've never heard of it being revived and certainly never shows up on lists of possibilities for Encores. There's just not much there when you take away the racial issue.
I'm sure I remember scenes from it performed on Ed Sullivan that gave a good sense of what it was like, but I can't find anything on YouTube.