I've contacted Qlik directly, as I could not find a answers to my questions. Following is what I have gotten back:
Is a dedicated GPU recommended or required on the server?
No, dedicated GPU is not required. Please check the same System Requirements page:
Also, QlikView Server does data-model calculation. Rendering happens on client side rather than server side. Hence GPU on server is not doing AJAX rendering(unless of course you are running browsers on the server). There isn't any recommendation regarding GPU on server from Qlik.
Is QlikView even capable of using GPU on the server for AJAX rendering?
As mentioned above, AJAX rendering happens on client side. GPU on server makes very little difference in terms of data-model calculation performance.
On the other hand, GPU on Client machine *may* help AJAX rendering. However that is depending on how OS and GPU Vendors are implementing GPU rendering as well as the actual browser's capability.