How will gluten allergy affect my digestive health?

None, if gluten-free. A person with gluten allergy (celiac disease) gets strong allergic reactions to gluten in the small intestine, which causes the lining of the intestine to lose its ability to absorb nutrients, vitamins, minerals, etc... If he continues to eat gluten, he can become anemic, lactose intolerant, and have diarrhea, tummy pains, vitamin deficiency, etc... Symptoms go away if he is on a gluten-free diet.
GLuten allergy. If you have celiac disease, then it is not a gluten allergy but rather an intolerance. Either way, with supplementing your diet with the nutrients and minerals from the gluten family, you should have a completely normal digestive tract.