Marketing Mix Model (MMM) using XGBoost?
Hi and welcome to the forum. As far as I know, MMM are causal models with the purpose of making statistical inference. This is the standard world of econometrics, where people stick to OLS or logistic regression since results are easy to understand based on estimated coefficients. 

Boosting (XGBoost is only one implementation of specific type(s) of boosting), is a technique which is mainly applied in predictive modelling since you have no "easy to understand" coefficients. So if your MMM application is not primarily about making a prediction, maybe boosting is not a good idea. However, you can still calculate pseudo marginal effects based on predictions, so there might be a way to make boosting applicable for inference (similar like inference is done in logistic regression).

It is not clear what you mean when you say: "due to that interactions effects are dealt with in a good way". Since boosting (usually) is based on very small decision trees, there are no interaction terms. What boosting does is, it focusses on "hard to predict" cases by weighting. So with boosting you usually get much better results (lower SSR, higher ROC etc) compared to OLS, logit etc. 

I don't know if and how boosting has been applied to MMM, but generally speaking, there are (in the moment) few applications of boosting in economics. So applying boosting can be innovative in this field, provided that you get it right. This requires a thoughtful definition of model requirements and objectives of the modelling approach.