Constitution bonuses aren't converted to Charisma.
As okeefe points out, undead in Pathfinder use Charisma to determine hit points, saves, and special abilities related to Constitution. However, that rule does not mention anything about replacing bonuses to Constitution with bonuses to Charisma. If you have a non-ability in Constitution, then you simply don't gain the effects of that bonus.
Also important to note, from the undead subtype:
Immunity to all mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms).
And from the Barbarian Rage entry:
While in rage, a barbarian gains a +4 morale bonus to her Strength and Constitution, as well as a +2 morale bonus on Will saves.
Note that undead are specifically immune to morale effects, and the Barbarian's Rage gives morale bonuses. In this case, regardless of whether or not the stat boost to Con shifts to Charisma, undead gain no benefits from raging. You may want to talk to your DM about houseruling some of this stuff if he wants your Barbarian friend to keep being effective.
There is nothing in the PHB or DMG that I can find that indicates that this is not possible.
However, because of this fact, this is a conversation you need to have with your DM.
It's possible that in the campaign they envision, there would be severe complications, it's possible that there won't be. But only they can determine whether or not this is a good idea for your game.
Best Answer
There is no general rule
There are no general rules for recovering from reductions to ability scores. Each case is taken on its own. Some, such as the reduction from an intellect devourer's Devour Intellect attack list no means of natural recovery. You must cast greater restoration to end this type of reduction. Some effects, such as a shadow's Strength Drain attack specify exactly how long it takes (emphasis mine):
A feature will tell you if there is a way to naturally recover from ability score reductions. Otherwise, there is no amount of time that can help you.