The power of the Buddha tooth does not depend on the genuinity of the tooth. The power come from the faith of the people. Therefore, if we believe and have faith, then it will have power.
Sharing a story on the importance of faith:
There was a mother in India that used recite the mantra of Buddha Chunda. The mother was recitING the mantra, the actual mantra is OM CHALE CHULE CHUNDE SOHA, but she has been reciting OM BALE BULE BUNDE SOHA, completely something else. But she was able to cook and eat stones, they became soft, cooked and she could eat. Probably, it means when there is a famine, no food, then this particular purpose of the deity, of course ultimate purpose is to become liberated from samsara and attain enlightenment. Her son who was a monk, getsul living in 36 vows, came home and heard her reciting the mantra, He told her the way she was reciting it was wrong, but when she tried to recite it correct, it didn't function to cook the stones.