No. If you have not enrolled in a Medicare Part D prescription drug plan, then you will not be eligible for the $250 Donut (or Doughnut) Hole rebate.
The $250 Doughnut Hole rebate is only available to people who are enrolled in a Medicare prescription drug plan and not receiving any financial Extra-Help.
Perhaps on the positive side, you will also never reach the doughnut hole since you will always be 100% responsible for the cost of your medications.
As a reminder, if you are currently eligible for Medicare, do not have some form of creditable prescription drug coverage (like VA coverage) and are not enrolled in a Medicare Part D plan - you may be subject to a late-enrollment premium penalty if you decide to join a Medicare Part D prescription drug plan.
We have more information on the Late-Enrollment penalty at this ling here:
https://q1medicare.com/PartD-Penalties-Beyond-Open-Enrollment.php.
We also have a few articles on the Late-Enrollment Penalty:
https://q1medicare.com/news/category/ Late-Enrollment-Penalty/11.html