No, you can't use Asus Suite III on your motherboard because it's actually not supported. I have checked the supported operating systems and the corresponding downloads, and Asus Suite III is not listed as being compatible. If it's not on the list, then it can't be used.
However, you can use ASUS AI Suite that's available in the Utilities menu.
Use the following link to reach the supprot page: https://www.asus.com/Motherboards/P6X58DE/overview/