If the child is listed as "Plus Infant" in the Passenger Name Record, it is technologically impossible to add a MileagePlus number to that "name".
However, if you want to give your baby a head start toward lifetime status, nothing stops you from purchasing a separate seat, even while under two years of age. However, that will cost more than the free (domestic) or heavily discounted (some or most international routes) ticket normally available for a lap child.
Unfortunately, you can't have it both ways.