There's nothing wrong with consuming protein before or during your workout. Some studies suggest that this may lead to enhanced results. Here's one example.
Other studies, such as this one, claim that this is not the case, though, and that while your body responds differently to exercise when you load up on proteins before the workout, this difference does not ultimately lead to increased muscle protein synthesis. It doesn't seem to have negative effects either, though, so do whatever you want.
Bottom line: It probably makes no big difference.
What probably makes sense though is to load up on carbs before the workout. Doing so will make sure you have enough energy to perform well and avoid a stress response (cortisol increase) during your workout. If you don't have enough carbs in your system during your workout, you will experience increased stress, while if you do your body will actually calm down. Your body is more likely to build muscle in a calm state than in a stressed state.
That said, the stress response won't last for very long, so it may not make such a huge difference if you wait until after the workout. On the other hand, insufficient energy may affect your workout performance, which in turn may affect how well you can work your muscles.
Here's a scientific review which discusses carbs before, during or after workouts. The general consensus seems to be that loading up on carbs before a workout may be a good idea, and loading up on carbs after the workout is practically indispensable.