Unfortunately, the answer is... Maybe.
Many modern graphics cards have displayed compatibility issues, either at the hardware (PCIe) level or the firmware (BIOS/UEFI) level, when attempting to use them with boards this old. This can result in the system not being able to POST (or boot) at all or the display simply not working until booted into the O/S environment. Unfortunately, there is no consistency to this; some boards work; others don't. The only way to tell is to get a board and try it. Perhaps you can find a store that will allow you to plug one into your system there in the store...
Hope this helps - and sorry I didn't have a better answer,
As mentioned before, in this case the only way to tell is to try the card. Old motherboards may show compatibility issues with newer components, that graphics card seems to meet the requirements of the motherboard; however, since it is too new it might nor work. If you decide to give it a try, make sure you are running the latest BIOS version; https://downloadcenter.intel.com/product/54876/Intel-Desktop-Board-DH61WW Downloads for Intel® Desktop Board DH61WW.
I would also like to let you know that we have a list of compatible devices with the Intel® Desktop Board DH61WW, find it here; http://www.intel.com/content/www/us/en/support/boards-and-kits/desktop-boards/000007439.html Tested Peripherals for Intel® Desktop Board DH61WW.