It will work, but it's not going to give you any breathing room at all. You are going to be toeing the line in terms of thermal compliance, even at the stock configuration. Overclocking will be out of the question. You would be a lot better off with a 360/420mm AIO or a 280mm or higher custom loop. One of the very big twin finstack air coolers would likely be sufficient as well.
For air cooling, this would be the optimal solution, for anybody desiring to go that way.
Various combinations of fans were tried on the NH-D14, especially the NF-A15 and the NF-A14. We found a winner.
www.overclockers.com
Or, in lieu of that, recommendations could include the NH-D15, D15 WITH Noctua iPPC industrial 2000rpm fans, Thermalright Silver arrow ibe extreme, Phanteks PH-TC14PE or Cryorig R1.
Otherwise, I'd recommend one of the larger AIO coolers AND plan to use a case with sufficient additional fan locations to allow for a good amount of case airflow to be implemented as CPU core temps won't be the only consideration. These CPUs are going to put the VRMs on most motherboards to the full test for sure.
I would probably not buy anything right now. Use what you have and determine for yourself whether or not the performance is sufficient for your demands. What works for you may not work for somebody else and visa versa.