If someone were to change his face through plastic surgery, would he become immune to the Death Note?
Looking at rule I:
This note will not take effect unless the writer has the person's face in their mind when writing his/her name. Therefore, people sharing the same name will not be affected.
Plastic surgery might stop photos of the old appearance from working, but unlike with the name, it has not been stated that the original appearance is required to kill a target.
Conclusion, No. Plastic surgery can not make one immune for the the death note.