Would this DP to DVI adapter work with eyefinity to add a third display on?

Solution
It should.

An active DisplayPort to DVI adapter should work because the Active adapter will generate its own pixel clock.

A passive DisplayPort to DVI adapter will not work because this simply puts the DisplayPort driver into a DVI Compatibility mode which cannibalizes resources needed for the other two displays.
It should.

An active DisplayPort to DVI adapter should work because the Active adapter will generate its own pixel clock.

A passive DisplayPort to DVI adapter will not work because this simply puts the DisplayPort driver into a DVI Compatibility mode which cannibalizes resources needed for the other two displays.
 
Solution