The valve used in this kind of setup is actually called a "foot valve."
Regardless, it's hard on the pump and less than recommended. A submersible pump would work just fine for this, and be less complicated. I notice in your drawing that you are pumping from the sump to the DT, yet you also state that you are using a separate pump. I'm sure you aren't forgetting to factor in the additional flow from the sump to the DT (if you already have other pumps moving water to the DT), and have made sure your drain system can handle it.
I'll give you the standard lecture on using a dedicated pump on a chiller though... IF you use a chiller with a outboard controller (as opposed to one that has the thermostat right in the heat exchanger), and your chiller uses a dedicated pump, a "situation" can develop. Should that dedicated pump fail, you aren't as likely to notice. Now, if the chiller's temperature probe is in the sump, and calls for chillin', the chiller can start running with no flow, and never stop, since the chilled water never finds it way into the system. That'll cause it to freeze, which will ruin your day.
That's why if you have an outboard controller, I recommend using either a flow switch on the chiller to shut it down on loss of flow (Aquatic EcoSystems has them), or use the main pump, because if it fails you are certainly going to notice it and be more likely to take action. Chillers that have internal controllers don't have this problem.