Yes, hair can grow back after a transplant even if it is shaved off before the procedure. In fact, it is common for the donor area (where the hair is harvested from) to be shaved or trimmed before the transplant to make it easier to extract the hair follicles.
After the hair transplant, the transplanted hair follicles may go through a shedding phase before new hair growth occurs. This is a normal part of the healing process and can take several weeks to several months. Once the hair starts to regrow, it will typically continue to grow normally.
However, it's important to follow your surgeon's aftercare instructions carefully to ensure proper healing and growth of the transplanted hair. This may include avoiding strenuous activity, wearing a protective headband or hat, and following a specific hair care regimen.