The answer is no. Only Indian citizens can operate a PPF account.
If you become an NRI while the PPF account is still operative and active, you can continue making contributions to it until the maturity period is reached. At this point, the account will have to be closed, and the proceeds will be deposited into your NRO account.
In case you renounce your Indian citizenship while the PPF account is still operative, the account has to be closed or deemed to have been closed from the end of the month prior to the month the one gives up his/her Indian citizenship. The deposited fund and any interest accrued shall be deposited into your NRO account.
Withdrawal from PPF upto 50% of the balance is allowed in the 6th financial year of the opening of the account. Premature closing of the account is allowed from the 5th year on proven educational and medical grounds.
See the following notification from the GoI: