I think it depends on what you are printing and how long in advance it is. I recently created an open faced book where I had a printed page (small print) that I had attached on a Friday afternoon. There was a faint blue hue to the background of the print on the icing sheet because of the paper I had copied the print from. By Saturday the blue was more prominent. So although the wording had not bleed, the coloring did change significantly. It didn't spoil the effect but next time I will print it off closer to when it is needed.
On the same cake I had printed a note that was laid on top of the book. It was a note I just typed in rather than copied from an actual book so I didn't have the background hue and there was no problem with it. So it all depends on what you are printing or rather where you are printing it from.
If you are concerned and have the time, print up a test, adhere it to a small cake and put it in the fridge. The you will be sure to not have any sleepless nights.