This would have some mechanical benefits for your character
If your arcane focus is physically attached to your body, this gives several potential advantages, the most obvious of which is that you cannot be forced to drop it. This would mean that, for example, a fighter's Disarming Attack would not be able to deprive you of your focus. Perhaps more importantly, if your party is captured and has all their items confiscated, it won't be possible for them to confiscate your focus (either that, or they will confiscate it very painfully).
In addition, you will be able to "drop" your arcane focus in order to grab something else without fear of losing it. For example, normally you wouldn't be able to stow your focus, pull out a weapon, and attack all on the same turn. Any character can do this by dropping their focus on the ground (a free action) instead of stowing it, but then they risk losing the focus if they aren't able to return to pick it back up later. With your focus embedded in your forehead, you will not run this risk, which gives you a little more flexibility in battle. Essentially, the hand with which you manipulate your focus will always be free to do other things in between casting spells. (I'm assuming you would still need to touch the focus with your hand in order to cast spells with it.)
All in all, these are minor advantages that probably won't come up very often, unless you specifically design your character around them by intentionally taking advantage of the ability to quickly switch what you're holding. If your DM finds these minor effecs acceptable, they could certainly allow you do run with this character concept. However, be prepared for them to say no if they feel it would be unfair.
In official Adventurer's League play, I'm pretty sure this would not be allowed.