Yes, it makes sense.
Az asztalok nem kint vannak has a meaning like, "The tables are NOT OUTSIDE [but they're somewhere else]."
Az asztalok nincsenek kint is more specifically about the absence of the tables. Omigosh, there aren't any tables!
Not exactly. :) There are tables (they exist), but they are not outside. That's all it says with "nincs". No contrast with "but somewhere else", as with "nem kint vannak".
You can use those two together in a sentence, no problem. But if they stand next to each other, like "nem van", they merge to nincs instead. It's like a mandatory contraction. Same with "nem vannak" becoming nincsenek. (All other forms of van stay intact, though.)