That's a possibilty. The records I looked at were at the NI registry office so would only have covered the 6 counties of Northern Ireland. If he was born across the border in Louth or Monaghan then it wouldn't come up.
The Carroll name does appear to be more frequent in Louth than Armagh judging by Griffiths valuation.
Sorry but I don't have ready access to the same records for Louth so can't help with checking that option.