If Y phenomenon is nfluenced by C and D variablesthen theoretical physical model Y = F(A,B, C, D) must be stochastic. So, your model is just an approximation of the needed model. You must to find a regression or ANN model, depending of the complexity, that include calculated value Yc= Y(A,B) C and D and to find a uploaded model for Y. Did you understand?

Yes it is possible and the related stuff also called as lag in ts analysis

If you include A, B, C, and D as inputs, then you can model the relationship between these four variables; whereas, if you include F(A, B), C, and D, you would be assuming that the set (A, B) is independent from C and D (think of it as a Bayesian Network).

Mathematically speaking, you can do this for a known dataset (i.e. targets are known to the user during training or testing). However, in real life scenarios, it makes sense that the prediction models were designed to assess targets for unseen data without labels. As a result, the model designed on the assumption that the labels could be incorporated as inputs will never work in this case, as it is a completely different model (y (a, b, c, d, y) is not the same as Y (a, b, c, d)). Also, if you know what to predict (y) why are you predicting it in the first place ?.

On the other hand, we can find a way to seed labels only in the training phase to provide more accurate results in the testing phase. in fact, we have already covered this topic in a recently published paper where we found a way to binifit from the labels information:

Article Leveraging Label Information in a Knowledge-Driven Approach ...