Searching interactions with RandomForest and/or GBM
Several times it does happen that interactions among variables improve the bias of the model. This is especially true when the effect of one independent variable on the target depends on the values of other independent variables.
I don't think there's anything mathematically incorrect in doing this.

E.g: let's say you are trying to predict revenue as a function of advertising. In this example it's reasonable to assume that the effect on revenue of one extra unit of advertising on Television  would depend on the existing level of advertising on Facebook (say). The true data generating function (if you had access to it) might be something like: $$Revenue=Ad_{TV}^{\beta_{1}}Ad_{Print}^{\beta_{1}}...$$ where $Ad_{TV}$ is the # advertisements shown on TV etc.
If you use provide the model the opportunity to handle such interaction terms you will be closer to modeling the true data generating function.

However adding more feature increases the complexity (capacity) of the model and you might have to use regularization wisely to prevent over-fitting