I assume the item won't because maxed out implies no more, but I am not sure if that only applies to leveling. I will save these items if they do in fact increase a maxed stat.
Stat up items will not have an effect if the stat is already maxed. Each class has their own stat maximums, and these items can't be used to get around that. If you're only a single point away from the maximum, the stat up item will only give you one point.
What you CAN do, though, is use skills. Skills bypass the normal limit by adding to the base stats, outside of the character's stats. The All Stats+2 skill, in particular, will make your characters much stronger.