Hi - new member. I was diagnosed with Crohn's about 3 months ago. Have lost ~40 lbs, typical symptoms, etc. My mom is a nurse who (ironically) works in a GI office (doing studies for a number of diseases...unfortunately none on Crohn's yet). She asked around in the office (per your question above), as I have a perirectal abscess as well.
The short answer that she received is: given the diet's purpose (to reduce the inflammatory response of body by reducing the amount of bad bacteria in the gut), the perirectal abscesses (which are a bi-product of this inflammation and the bacteria) would theoretically be reduced / eliminated in the event the diet successfully manages to cut out the inflammation. Keep in mind, neither her, the GI's that she talked to, or myself are purporting to understand this fully or argue that it is 100% accurate (I know, these statements suck, because everyone wants a solution, but it's just not a reality...)
I myself have been on the diet for 2 weeks and have been enormously successful in reducing D and bloating. I have been approaching it slowly...adding foods in when I feel ready. My strategy was to add in one "lighter" food followed by one "heavier" food....i.e baked apples / pears followed by avacados (rich in calories and nutrients).
Now, I eat avacados like they are going out of style.