It does not prevent treatment, but if treated with antibiotics, that animals milk will never there after be organic. Thems the rules.
In Europe it’s different - https://ec.europa.eu/agriculture/organic/eu-policy/eu-rules-...
“When the animals are ill, chemically synthesised allopathic veterinary medicinal products including antibiotics may be used where necessary and under strict conditions. This is only allowed when the use of phytotherapeutic, homeopathic and other products is inappropriate.”