It depends. Most surgical management of the bunion deformity at the joint of the first metatarsal is called joint preservation surgery.  These corrections allow the surgeon to place the joint back into anatomical position, which allow you to continue to wear a reasonable high heel.

Conversely, sometimes the joint at the first metatarsal is so arthritic that it may require a surgical fusion, this no longer allows the joint to bend, making high heel shoes difficult to wear.