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Well as you say antoxidants are an important weapon in mopping up free radicals which cause damage at the cellular level. These are very important for all animals.
There are many, many, anti-oxidants in nature and I would expect that most dairy cows fed correctly get plenty.
The guts of the mastitis problem is the fact that modern dairy cows are bred to produce massive amounts of milk and fed massive amounts of food so that they do. This creates a weakness in the mammary glands and the intestines which results in lower immunity and infection of various types.
I agree, and so would most of my colleagues, that it would be wonderful to reduce, or cut out completely, the use of antibiotics. I cannot see a process that merely stimulates an already present immune system on an already stressed organ being that revolutionary. I need to see more, relevant, trials where the experimental process is accurately depicted.
I do agree that it probably does seem to have benefits but can't see it being the "magic bullet" for mastitis and replacing antibiotics.