I've just taken a bunch of photos without realising that my Nikon D5200 camera's 'color sketch' mode was enabled. Is there any way to revert them to real, effect-free photos?
No. Effects are almost all irreversible. This is because the vast majority of them remove details, gradations and color. Sketch look removes color-variations as do most types of painterly, pop art, etc effects, depending on the camera. Even something like the miniature effect blurs details out of most of the image which makes them unrecoverable.
Now as @Philip said, if you have a RAW file, then the effect is not applied on your data, only shown as processing. This lets you reset and do your own processing to produce a more natural looking image.
Where you shooting in RAW or RAW+JPEG mode? (assuming you can even shoot RAW with the effects mode enabled). If so, then it will just be a matter of re-processing the RAW file. If not, the answer is almost certainly "no" - it may be possible to "undo" some of the effect via Photoshop or your other favourite image editor, but it's almost certainly more trouble than it's worth unless these were really valuable photos.