Yes for damaged stones, if they are simply broken.
The text regarding the cracked stones and is not simply flavor text. If an ioun stone is damaged, it will be automatically downgraded to a cracked ioun stone, because it gains the broken condition.
These stones bear an obvious crack, whether as a result of the crafting process, because the raw stone was already cracked, or because the stone has been damaged (for example, if it gains the broken quality). A cracked stone’s power is usually the same as an undamaged stone, but weaker.
These cracked ioun stones are simply damaged magic items:
A damaged magic item continues to function, but if it is destroyed, all its magical power is lost.
As such, you could repair this broken condition with magic:
If the item does not fit into any of these categories, the broken condition has no effect on its use. Items with the broken condition, regardless of type, are worth 75% of their normal value. If the item is magical, it can only be repaired with a mending or make whole spell cast by a character with a caster level equal to or higher than the item’s. Items lose the broken condition if the spell restores the object to half its original hit points or higher.
Once this crack is repaired, the stone is fully functional again.
However, keep in mind that for ioun stones not created during play the GM has the final word whether the crack was made from damage on the magic item, or from a poor choice of materials, or something bad that happened during the creation process. This is important for the game balance as well, you will have trouble with the Wealth by Level if the players repair that 1,000 gp magic item and turn it into another item that is worth 200,000 gp (like the Pale Orange Romboid).
So, a cracked stone you find as loot might not be repaired because it wasn't damaged, but was made from an inferior crystal. While one that got damaged during play would be downgraded to their cracked version, and you could repair it back using Mending or Make Whole.
No for other inferior stones
Inferior ioun stones, on the other hand, are not broken, they are simply inferior from their creation, either in quality or in magic power. And although you can still upgrade them (with GM fiat) using the normal rules for Crafting Wondrous Items, all inferior stones are effectively different items from their regular counterpart.
Magic items that are depleted lost all their magic power. There is no clear definition of the term under the rules, but it is used as a synonym of when the magic item's power is spent and cannot be used again, like on the Helm of Brilliance:
The helm may be used once per round, but each gem can perform its spell-like power just once. Until all its jewels are depleted (....)
Once all its jewels have lost their magic, the helm loses its powers and the gems turn to worthless powder. Removing a jewel destroys it.
Which normally means you can still use the mundane object as part of the materials for a new magic item, but the original source of power is now gone. A wand that has used all charges is still a pretty stick with cool-looking runes carved on it, you could even fool someone without access to Detect Magic that it is still a powerful magic item.
Seeker of Secrets (page 46) also says that the effects of an ioun stone cannot be changed after creation (credits to @HeyICanChan):
For stones that have multiple possible effects (...), the exact effect is determined by the item crafter when it is created and cannot be changed thereafter.