Only one way to find out...
Kidding. The 1600X is a 95W TDP chip, so it will probably be not sufficient to cool it. There is a reason why they didn't include a stock cooler, since it is 95W TDP. Other Ryzen chips (1700, 1600, 1500X, 1400 etc) are 65W TDP, the Wraith spire is a 95W TDP cooler. So if they were to pair it with the 1600X, they know that it won't be enough for the chip. So that's why they did not include a cooler with the 1600X.
If they were scared to include a cooler for the 1600X, do you think the Phenom II cooler is enough?