Yes—the usual DOF standards are based on assumed viewing conditions, often something like an 8×10 print viewed from a typical distance. That means they are only approximations.

For larger displays or larger prints, the acceptable blur circle effectively gets smaller, because any blur is being enlarged more. So an image that seems sharp enough under “typical print” assumptions may not look as sharp on a big 4K screen viewed closely.

In practice, the best way to judge this is to evaluate the image at the final output size:

• Resize/export the image to the target display resolution, such as 3840×2160.
• View it at 1:1 pixel size on screen.
• Check important in-focus areas and decide whether the detail looks acceptable at the expected viewing distance.

If you are shooting specifically for demanding viewing conditions, don’t rely only on a generic DOF calculator. Bracket focus and/or aperture when possible, and inspect images at maximum enlargement on the camera LCD or later on a monitor.

“Acceptably sharp” is still somewhat subjective, but judging at the actual output size and viewing distance is more reliable than relying on standard print-based assumptions alone.