Yes, but you didn't say they didn't build the greaat wall. Though the Great Wall in some form did exist in some form long before the Ming, the Ming did build it to its greatest extent. And I have literally never referred to the Great Wall in this comment chain. As for your purposes, sure. It was meant to do those things, but there is no evidence it meaningfully slowed down any invasions, the second goal could have been accomplished just as well by the preexistent series of border outposts, and it's effect on the nomad economy is questionable. There is certainly a correlation between the crash of their economy and the construction of the wall, but it is nowhere near a direct correlatiom, and the causative factor likely rests with the Ming's much less friendly trade policies, as well as the continued decline of nomadic military and political power following the fall of the Yuan in the East, the khanates in the West, and the Silk Road system of trade routes that connected them.