"Unwarping" Old Oak

Sometimes a cup warp can be corrected if the warp was caused by short term improper storage where moisture has gotten to one side and not the other by wetting the cup side. If you have some that has sit for years and warped I think the only solution is flattening on a jointer and surfacing.

Try putting a test piece in the sun and see what happens.

In answer to the you question, NO. If it is that bad, you should burn it. Seriously. You can try and save it but it is not worth the time or blades to do it. Cook something.

Let it sit for a while in a protected area off the ground so air can circulate around all sides. This is so moisture content can stabilize throughout the piece. This may take a few weeks for 1x stock, longer if thicker.

If after this the piece is still warped, I agree, that's the way it wants to be and there isn't much you can do about it.

If you do decide to plane it, wait until it is stabilized.

wet the grass and the cupped side and place in the sun for a few hours. If really bad you could even but some weight on it. I have un warped a few pieces but it never will be perfect.

If it has been warped for a long period, flattening is almost always unsuccessful. The cell structure will be permanently formed and can not be forced to change.