Correct. But nobody who is aware of the Catholic religion and EECNS, yet refuses to convert, is covered by that tiny umbrella of “desire”.
Not exactly as tiny as you might think.
The Council of Trent anathematized all Protestants, but that’s easily taken out of context.
At the time of the Council of Trent, all Protestants lived in traditionally Catholic lands, and had been raised up as Catholics, instructed in the Catholic faith. To become a Protestant was to literally wage war against the Catholic Church: Calvin prohibited the Catholic mass and Luther proclaimed that real Christians should rather be conquered by Islam than remain under the Vatican. (Yes, he changed his mind about that.)
Contrarily, by the 2nd Vatican Council, Protestants were mostly raised as Protestants, by Protestant fathers and mothers, taught Protestant theology and taught layers upon layers upon layers of counter-Catholic doctrine, interpretation, and even vocabulary. How much easier it is for someone to deeply desire Christ but yet be held back from the Catholic church, than from the days when assassins of children were celebrated as Protestant heroes!