So I did buy a ticket but was told that only the "adult" part is finalized (I can see it in my list of trips). I was told that the infant ticket will be mailed in a few weeks. There is no charge for it on my credit card charges yet. I guess I have to have faith Delta won't forget about it.
This also happened to me on my two bookings, one using DL miles on Air France, and the other using DL miles on DL metal. I booked the trip, then was on hold for a while waiting for a quote of fares from the international ticketing desk. Got the quote, and said that it would be processed separately and I'd receive the tickets in the mail. Took a few weeks, but eventually was charged and got the paper tickets in the mail. For the Air France one, it was weird as the confirmation and paper tickets came from KLM, while the adults were all DL.