Only if he wasn't scheduled by his Bishop to say another Mass. Priests can't just go about choosing how they will say Mass one day to the next. Take a bi-ritual priest. He can't go to a Byzantine Church and claim a "right" to say the Latin Mass there just because he has the canonical power to say both rites.
The right of priests to say the ancient Mass is universal. It knows no diocesan boundaries. It was granted by Pius V and has not been officially abrogated; therefore any attempt by an Ordinary to punish a priest for saying this Mass would be illegitimate. No bishop can oppose a papal bull which explicitly prohibits the punishment of any priest who says the Mass.