Very unlikely. Covered puts could only be covered by a short position in the stock. To sell a covered put, the employee would have to own a short position in the stock. It's typical that incentive-stock agreements will prohibit the employee from taking or holding any bearish equity/derivative positions. Shorting AAPL would violate that employee agreement.
You probably meant calls, not puts. If you did indeed mean calls, it wouldn't be a covered position unless he owned the underlying stock, which he won't until he vests and exercises. And if he did own the stock, selling the call against it would be considered a bearish move, and thus prohibited by the employee agreement.