? No, you need to educate yourself.
The gestation period of a cow is approximately 9 months, similar to humans, by coincidence. Only a cow that has given birth to a calf will produce milk. The normal lactation period is 305 days before the cow is "dried up" before giving birth again. 10,000 pounds of milk is considered a good lactation total. Typically, cows are bred to calve once per year. Typically going through 10 lactations before that one way trip to MacDonald's.
Dairy bulls are notoriously nasty creatures, so artificial insemination is almost universal in the dairy industry. The "tract" that you speak of is the cow's colon. The technician is careful to guide the pipette so as not to injure the animal, and the colon provides convenient access to feel what is going on inside.
If you are squeamish about such things as cow's colons, then vet school is not for you.
I was speaking from the perspective of the people in my opening sentence. How commonly known would you suspect those facts are in your comment?
e.g. "[They might assume] cows simply produce milk like chickens lay eggs."
It's normal to never really think about it -- our society is set up so that you never have to. The secretion comes in a jug, the meat comes in cellophane, and that's it.