I put one on a cake and it still looked good 2-3 days later.
It should be fine if the cake is for Tuesday morning and you put the edible on Monday night. I have done this several times, it gives the edible a chance to blend in very well with the icing, and should still look great in that small amount of time!
LIGHT is a lot of what seems to make edible images, especially the ones with bright colors, fade.
HUMIDITY from being in a refrigerator could also cause you some problems, the cake can sweat after it is removed and could cause the colors on your image to bleed or run. So I would advice leaving at room temperature if at all possible.
Just my 2 cents, HTH!
ive put it on the night before as well and it hasnt deteriorated.
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