At best it could only be a very rough estimate.
Why is this so?
Because ultimately depth of field depends on factors that the camera does not know and which may be, and often are, changed after the image is captured. Among them:
- Display size. The more an image is enlarged from the size of the image projected by the lens onto the camera's sensor, the more the blur in the photo will be enlarged. Things that look like a single point when viewed smaller can be seen as blur when viewed larger.
- Viewing distance. The further a viewer is from a displayed image, the deeper the depth of field will be. As the viewer moves closer amounts of blur that looked sharp from a greater distance can be seen to be blurry.
- The visual acuity of the viewer. A person with 20/15 vision can discriminate blur from points that a person with 20/25 vision can not when the display size and viewing distance are the same.
You can play around with these variables along with focal length, subject distance, and aperture using the Flexible Depth of Field Calculator from Cambridge in Colour and clicking show advanced.
Back when 35mm camera lenses had depth of field markings on them the unspoken assumption was that the 36x24mm size image from a piece of 135 film would be displayed at 8x10" size and viewed from a distance of 12" by a person with 20/20 vision. Photography courses at the time, at least the good ones, taught that for larger display sizes, the DoF would be narrower. If we doubled the display size from 8x10" to 16x20", for instance, the DoF would be halved.
In a digital environment the assumption that everything will be viewed at 8x10" from 12" is no longer valid. So is the assumption that a particular lens will always be used with the same sensor size. When someone looks at a 24MP image on a 23" HD (1920x1080) monitor with a pixel pitch of about 92 ppi, one is looking at part of an enlargement equivalent to a 65x43" display size!
A little background on what depth of field is, and more importantly what it is not.
In a way, depth-of-field is an illusion. There is only one plane of focus. Everything in front of or behind the point of focus is out of focus to one degree or another. What we call DoF is the area where things look, to our eyes, like they are in focus. This is based on the ability of the human eye to resolve certain minute differences at a particular distance. If the slightly out-of-focus blur is smaller than our eye's capability to resolve the detail then it appears to be in focus. When you magnify a portion of an image by making it larger or moving closer to it you allow your eye to see details that before were too close together to be seen by your eyes as separate pieces of the image.
Since things are gradually blurrier the further they are from the point of focus, as you gradually magnify the image the perceived depth of field gets narrower as the near and far points where your eyes can resolve fine details moves closer to the focal plane.
If you are viewing the image on the camera's built-in screen there is something else going on as well. A typical DSLR sensor may have a resolution of about 20MP. A typical screen may have a resolution of about 1MP. Some of the the detail in the image the sensor recorded is being combined to fit on the lower resolution screen. And although I've never read this, I think that camera manufacturers tend to sharpen the images as much as they can for the camera's screen so the pictures will look better to the photographer.
For further reading:
Is camera lens focus an exact point or a range?
Why did manufacturers stop including DOF scales on lenses?
Is there a 'rule of thumb' that I can use to estimate depth of field while shooting?
How do you determine the acceptable Circle of Confusion for a particular photo?
Find hyperfocal distance for HD (1920x1080) resolution?
Why I am getting different values for depth of field from calculators vs in-camera DoF preview?
As well as this answer to Simple quick DoF estimate method for prime lens