Canonically, it's unclear.
After scouring every 2nd edition product mentioning the Gray Waste listed in the Planescape Index, I'm confident that while a person can be rescued from the late stages of the plane's apathy sickness, it's not clearly defined whether they recover from the graying effect or apathy effect, or how quickly it might occur.
The primary source on the Gray Wastes in 2nd edition is Planes of Conflict (1995), Liber Malevolantiae p.42-64 and Player's Guide p.30.
Planescape Campaign Setting (1994)'s A DM's Guide to the Planes, p.59, asserts that rescue is indeed possible:
Each week, travelers must succesfully save vs. spell or be trapped on the Gray Waste, unable to muster the desire to leave. Once trapped, a body becomes a larva in 1d6 months. Despairing travelers must be rescued by others if they are to be saved.
Of note, this is different to the 3e Manual of the Planes, which asserts that the change occurs instantly on a failed save and thus allows no chance for rescue. In fact, according to Liber Malevolentiae p.44, there are groups of heroes who rescue people in this manner:
It's for this reason that certain groups of good folks make it their job to track down sods afflicted with the soul-wasting sickness of the Waste. These do-gooders want to save as many from the horrible fate of larvaedom as possible, and to keep the cursed fiends from gaining new recruits.
The only clue suggesting long-term persistence of the apathy effect is that Planescape Campaign Setting p.59 suggests that even those who leave the plane suffer some permanent debility:
That despair eventually reaches into the heart of travelers who stay too long, sucking a little life from them, too. See a berk with a dead-looking stare and he's a gloom-bug of the Gray Waste, for sure.
This suggests that at least some people suffer long-term debility and do not return to normal, although the possibility is still there for them to eventually recover, or for some to recover, and there is not really any mechanical definition for this debility.
Planes of Conflict Player's Guide p.30 describes that the plane's influence can be stopped using charm spells, and that taking people from the plane can prevent a relapse:
It snaps a berk out of whatever sad reverie he's in, bringing his hopes and desires flooding back in a great rush. He's absolutely grateful to the caster for as long as the spell continues; when it ends, he'll hate the caster because he sees the spell as the manipulation it was. And then he falls into an even deeper funk if he's not taken from the plane right quick.
Hellbound clarifies that charm spells work by temporarily restoring the creature's faith in life, shielding them from the plane's apathy effect. Unfortunately, Liber Malevolantiae p.46 says that charm spells have no effect on creatures suffering the sickness for more than two weeks, and it also warns that it's a temporary fix:
But once his anger fades, he sinks even futher into despondency, and he automatically fails his next save against the Waste's spiritual numbing. From there, it's just a matter of time.
The sources don't say anything about recovering, except to describe it somewhat poetically as a "tan", which might suggest it is a temporary change in color. Consider also the lack of NPCs described as permanently colorless from visiting the plane, and that adventure modules set in this plane don't mention permanent graying as a side-effect; e.g. the Great Modron March doesn't turn the modrons gray. This suggests that graying out is unlikely to be permanent, though again, it's unclear.
Finally, it's legitimately possible that the apathy effect isn't even true, or doesn't work as described. Liber Malevolantiae p.44 warns that, in true Planescape fashion, everything about this wasting disease could easily be a myth invented by a yugoloth.