No, the solution is not saturated.
Your tool of choice here will be the solubility graph of potassium nitrate,
The curve shows you the amount of potassium nitrate than can be dissolved per
For the sake of simplicity, let's assume that the graph shows the solubility of the salt per
Now, if you draw a vertical line starting from
This represents the solubility of the salt at this temperature. In other words, you can only hope to dissolve
Your solution contains
#"200 g"color(white)(.) - color(white)(.)"30 g" = "170 g KNO"_3#