Yes, it can. Implant placement can actually numb your jaw if an implant is placed onto a nerve.
In your lower jaw, there is a big nerve running through. If you hit that nerve, that nerve can go numb.
Your face will not droop, it’s not a motor function, but you can feel a very strange sensation -- like after you go to a dentist and they inject your jaw and it feels a bit numb.
An implant can cause permanent numbing. That’s why it’s very important for your dentist to do a preoperative evaluation with x-rays or 3D scans to see where that nerve lies.