DD's pediatrician is a firm believer in this theory and she used it on her youngest child (her older two are allergic/have eczema) with great success.
So I was put on a very restricted diet from day 1. No dairy at all. Since both my family and DH's family have a history of severe allergies, I was also instructed to eliminate many other foods from my diet.
I didn't have any dairy until after DD's 2nd birthday. Talk about tough!
Anyway, at around 3 months, DD developed eczema. It was not very severe but she did have it constantly for a long time with varying degrees of discomfort. The rashes were mostly behind her knees. I think she started growing out of it finally after turning 2.5 y.o. or maybe closer to 3.
I'm still careful with the laundry detergent I use for her clothes, but she has no diet restrictions now (she's turning 6 in October) and the eczema has not reappeared. She has not developed any other allergies.
So, basically, from my experience I cannot be sure if it helped, but I'm sure I'd do it all over again because I do feel it helped with the overall allergies.
Take care.