[Non-Sequitur]

Did the "Vatican State" even exist in 1861 as a valid nation-state?

It certainly did...sort of. What was left of the Papal States was a protectorate of the French at the time, whose troops kept King Victor Emmanuele from occupying the Patrimonium Petri. So the whole diplomatic recognition thing and that stuff about protecting confederates makes for an interesting, if not totally accurate, story. The Pope wasn't running the whole show at the time.

[mac_truck]

A review of the Vatican Secret Archives reveals no mention of any recognition given to the Confederate States of America.