I did book international award ticket for my wife and I with lap infant on the website recently. The trip is still upcoming but I got confirmation quickly and automatically with all of us on the same PNR, but all three of us have separate eTicket numbers - not sure if by "confirmation number" folks are referring to the PNR/record locator or the eTicket numbers.

Now last fall when I booked a international paid ticket and did not initially add the lap infant, they had to put the infant on a separate PNR and linked it somehow to our PNR. I will say that things did not go smoothly. First it took a long time over the phone to create the infant record, then since I wanted to make sure to get a paper receipt it took just as long at United club desk for them to figure out how to apply payment for the fee and generate a paper receipt. Then on actual travel day, even though I had all the valid reservations showing up on the website and printed out, plus the printed out paper receipt directly from a United employee, there was some problem the check-in agent could see with the infant boarding pass that the gate would not accept it. It was some extra letter like "A" printed on the boarding pass that the sympathetic check-in agent knew would be rejected by the gate agents. It took 45 minutes standing at the check-in counter with a cranky toddler,for the agent to work with a back-office by phone to properly fix the reservation and print out a valid boarding pass.