The OHOTMU Master edition for Wildheart lists him as "Superhuman Regenerative" Defined as: "Able to regenerate injured tissue and brain cells to an extraordinary degree; but not able to regenerate missing limbs or organs..." I have no specific info on his current regenerative abilities, they may have since increased.
Sabertooth told the Weapon X doctors to "leave out his chatterbox", I'm assuming telling them not to try to repair it, and, with Sabertooth long gone from Weapon X and Kyle still mute, I'd assume his healing factor hasn't been able to replace his missing vocal cords.
It remains to be seen if any of the writers at Marvel have the heart to give him his voice back...I doubt it... [-o<
And taking away his voice ruined one of his main charcter traits, his sense of humor, the constant joking, witty observations...