Putting it simply.....No, not eating until you waste away would not fix Increased Digestive Permeability. Commonly recommended supplements such as Glutamine will also not fix IDP.
IDP is caused by an infection which is protected by a biofilm. It is the biofilm which causes the IDP and not what is commonly believed to be involved. Destroying the infection at the primary infection point allows the digestive system in multiple places, both the point of infection and also usually the colon, typically the transverse colon to heal. The infection prevents the digestive system from healing and it also presents the normal production of digestive mucosa.
You might find that not eating could lessen the effects of IDP such as immune system reaction and autoimmunity.