Quite basically, yes, and they can have intolerances too.
Whilst pregnant last year, my allergies/intolerances seemed to reduce in severity. Initially they got worse, then as the pregnancy progressed they improved and I didn't react anywhere near as violently as I had done previously - hence the drop in the blog submissions!
It now seems that my 3 month-old baby who has not stopped coughing, wheezing and having snuffly nose since being born - may have a dairy allergy. Not to my milk but to the few milk proteins that are passed on to her through my milk. Other allergens which can be passed on through breastmilk are wheat, eggs, citrus and peanuts.
I rarely eat peanuts so it has to be something that I have in my diet every day. My egg allergy was disgnosed at 6 weeks old, so for now I will be going wheat, dairy and egg free again, in the hope that it will help clear up my snuffly baby.
An interesting article called "Milk: Does it Really Do a Body Good?" written by Dr Jay Gordon can be read at http://www.avoidingmilkprotein.com/milkdrJ.htm. It is quite informative and discusses the contents of milk, symptoms of intolerances/dairy and reactions of breastfed babies to changes in the diet of their mother,