The only reason I can imagine it would be detrimental is when you strain your eyes trying to "see" the illusion, it could harm your eyes.

No.

I was asked to solve a problem by finding a hidden clue in one of the 'magic eye' images. I have never been able to see the 3d effect in this process. Finally, today I did it. I am nearsighted and suspected my glasses were interfering with the effect so I removed them. I placed the image(monitor) about 14" away and focused about 30" away and finally got a lock on the 3d image! I numerical coordinates appeared to be raised about 1.5" above the background which appeared to be about 22" away from me. This was with very relaxed focus and casual viewing. Interesting that everything around me was unfocused except the perceived image which was outside of my normal range of focus yet was sharp. After I got the numbers, I couldn't focus on the paper to write them down clearly, what a mess but there they were. I put my glasses back on but couldn't focus on anything closer than 10 feet away. It took almost 5 minutes and some strain to be able to even focus on the computer monitor again. I am going to experiment further. Such an exercise may be benefitial for retraining eye focus to regain some lost abilities that are being compensated for by the glasses.

Optical illusions work by tricking the brain - not by interacting with the eyes. In this respect they're more like passive windows to the brain.