I heard this from a friend: she told me that a friend of her's would always sneak his dog onto the flight. He would sedate the poor baby and sneak him in a bag. Well, he got caught one of those times and the airline told him that he couldn't fly with the dog. He could either miss his flight or not fly with his dog. So, this guy ended up giving away his dog to some random person at the airport because he didn't want to miss his flight.
I wouldn't risk it. I believe people have tried to put 2 doggies onto the same flight without telling the airline of the 2nd dog. But these people do call in to reserve a spot for their baby. It's just the 2nd one they don't mention because some airlines have rules of only 1 pet per person.