Protein before/after training will increase protien synthesis over and above the increase caused by training itself.
The addition of carbohydrate replaces muscle glycogen used during training, which can be a lot especially on full body HST style routines. It also increases insulin, which helps protein synthesis by increasing amino uptake, and it also inhibits the post training rise in protein breakdown.
While you could argue that the carbs will reduce fat oxidation after the training session, but overall it wont make a difference as long as its all factored into the calorie intake