"Career stats" are not a concept which are rigorously defined by the Laws of the Game, so anything here is going to be based purely on how your chosen stats provider chooses to count things.
That said, we can look at how Cricinfo handles this situation. In the first Ashes Test of 2005, James Hildreth caught Ricky Ponting while on as a substitute fielder:
27.3 short of a length and outside the off, Ponting cuts but it is uppish and straight to the man at point. James Hildreth, the substitute pouches the simple chance and that's the end of Ponting! 102/3
It is easy to tell that this is not recorded on his career statistics as Hildreth never played a Test Match. While substitutes and 12th men aren't quite the same thing, they are very similar once the toss has been made and the teams decided.