The title says "all of Christendom", which is NOT feasible, at all.
The first post says "all Catholic nations", which is. Although even that's hard. However Charlemagne's empire, the original HRE, was supposed to be that. You probably can't avoid a split or two, but maybe they can be re-united (by conquest or by marriage).
If they can do THAT, and avoid the mini-collapse after the first blooming, you might get it to expand so that it did, in fact, include all Catholic nations.