Having studied paper conservation a bit, the main concern would be exposure to acids that typically were used in cardboard. If the tube stayed in relatively stable temperature & humidity they might be ok.
Comic collectors deal with paper degradation issues often. They have something called an OWL gauge that is a set of colors that indicate how yellow the low grade paper has become due to acids in the paper.
One way to make a general guess of this would be to put a piece of white printer paper or equivalent next to the print background and compare the two.
Otherwise, things to watch for are brittleness of paper, creases, tears or stains. Conservators usually store valuable prints flat in acid-free containers, but sometimes time is kind to an old item.
Hope this helps some.
