A similar thing happened in my family generations back - one granny simply took an infant round to the Priest and had it done there and then! So the dad went to the methodist minister and did the same! But things were different in those days.
I think Macca that this will come down to an individual priest's discretion. As a matter of philosophy I don't think a priest would refuse to baptise an individual, but it may be that with an older child he will expect (or the diocese may have regulations) that the child is involved in some pre-baptism talks to establish his own outlook and to explain what this means spiritually.
There has been a surge in later-child baptisms to get children into faith schools: if this is behind your ex's purpose then look to whether this is a benefit or a hindrance to the lad in the future. Knowing what I know now, I would have done this for my (now adult) children.