If you X-rayed the cube with the card on top or bottom, I wonder if the card would be distinguishable? I imagine that, if the cube was on one of the sides, it'd be practically impossible to see.
http://rusolut.com/wp-content/uploads/2014/02/msd1xray.jpg
And an xray of a rubiks cube:
https://c1.staticflickr.com/5/4138/4859926370_10d2a0d071.jpg
Overall, doubt you could see it without looking very carefully.