It’s very much possible and indeed such a problem that it may be done by mistake if a large enough data set isn’t used (see overfitting). A model trained to output just this one image will learn to do so and over time it should learn to do it with 100% accuracy. The model would simply learn to ignore whatever arbitrary inputs you’ve given it
That probably doesn’t count as “AI” do… It’s more a very bad form of compression (that may very well make the image file larger)