No. A growing degree day model predicts biological events based on accumulated thermal units. It can be used to predict when plants will break dormancy, flower, set fruit, or how quickly a pest will develop and complete its life cycle.
An herbicide might be more effective against a plant at a specific life stage. In such cases using a GDD model might assist better herbicide usage. But they do not interact.
Yes. You are studying long term effects of sublethal doses of herbicide. The effect of the sublethal dose changes as the plant matures, and a growing degree day model could help as a simple model of plant physiology. In this case there could be an interaction -- but this approach to understanding herbicide action is uncommon. However, see studies on hormesis (https://en.wikipedia.org/wiki/Hormesis).
GDD units have no contribution of the efficiency of herbicides. Although, herbicide is effective when it is applied at certain crop stage, that is possible to predict using GDD approach. Hence, GDD can be useful in decision making of herbicide application in a particular crop.