Obviously Christians in full communion with the Catholic Church fully participate in the body of Christ.
As long as Catholics don’t die unrepentant in a state of mortal sin, and refuse God’s mercy at the time of death. We can cut ourselves off from His Body permanently, if we really want to.
What about other baptized Christians? Do we say they are also joined to the Body?
A validly baptized Christian is part of the Body of Christ. Same mortal sin thing applies.
What about non-Christian people of goodwill?
That would be between them and Christ. God knows their will, and He will not make them be part of Him if they don’t want to be. If they really want to stay in mortal sin and are unrepentant, that’s their choice. If the Lord wants to preach to them mystically at the moment of death, that’s His choice. But obviously it’s better to be a baptized Christian than not, all else being equal.
Further, is the Baptism of a Desire applied at death to those deserving of it, or can they receive it earlier in life?
Baptism of Desire only happens if you die unbaptized but fervently desire Baptism. (Like catechumens who are martyred.) Since even non-Christians and non-theists can validly baptize, most people who want to be baptized can manage it, given time.
God can of course give gifts to anybody He feels like, so many unbaptized persons who believe in Him receive various benefits from Him. But that’s by His choice, and isn’t promised. These gifts are not the same as Baptism’s gifts, either.