Can a vegan/vegetarian diet help with recurring gastroenteritis?

Yes it can: Depending on what you are eating. Light healthy vegetarian diet is good for GI health. Rice and lentils are good source of carb and protein during diarrhea, make sure eat plenty of yogurt and probiotics for good bacteria.

Possibly: But it may make it worse, depending on the cause. Most bacterial food poisoning and gastroenteritis occurs with animal products. Avoiding "food, inc's" processed livestock products will reduce that. But if you have food sensitivities, they may come from vegetables or grains and cause similar symptoms. For example gluten sensitivity or celiac disease from wheat can cause GI symptoms.