It is! Here is an amazing review from 2011 that literally has all the answers. I'm not kidding, all of them. I would marry this review if I could.1 It also includes information on other animals.
The main takeaway is that IgA from milk is not readily absorbed by the infant body. Secreted IgA is mainly to provide a protective coating for the mucosa while the infant is developing its own nascent immune system. IgG passed along from the placenta (your other question) provides the main source of absorbed antibodies. As it says in the review:
Milk sIgA is not taken up by the infant’s intestinal mucosa. In fact, gut closure in humans occurs before birth and little immunoglobulin is absorbed intact in the intestine after birth. However, the presence of sIgA in the intestinal lumen is part of the protective function of the epithelial barrier in the intestine... Secretory IgA is considered to be the primary immunoglobulin responsible for immune protection of mucosal surfaces such as the intestine.
In terms of enzymatic activity, the digestive system will in indeed chomp up the antibodies; that's part of the reason breast feeding should continue as needed. That's okay, because there's plenty to go around:
Much of the immunoglobulin consumed in an immune milk can be expected to be partially or completely digested, however some portion of the immunoglobulin will remain intact or at least partially intact and capable of binding to an antigen.
It turns out that immunoglobulins are moderately resistant to digestion, at least more so than other milk proteins. There's a section in there detailing some experiments where Ab was given to individuals:
In adult humans consuming a bovine whey protein concentrate, approximately 59% of IgG and IgM was detected by radial immunodiffusion from effluents from the jejunum, while 19% was detected in the ileum. These estimates of digestion of immunoglobulin compare with estimates of digestion of milk proteins in adult humans which are approximately 42% complete at the end of the jejunum and 93% complete by the end of the ileum, again underscoring the relative resistance of immunoglobulins to digestion in the gastrointestinal tract.
Digestive enzymes vary as to which antibody they prefer to digest, but at least some of them will technically digest the antibody, but still leave functional Fab fragments, which are still immunologically active and useful to the infant immune system.
1: Did I mention I love this review? I love it.