It depends on how hard they both try.

Go give it a shot at Nunitii Latini click on the "Kuuntele" button. This today's news spoken clearly in classical Latin with a slight Finnish accent.

Even to English speakers there are a lot of cognates that you can pick up. You will probably hear "Americanorum" and have an idea, even if you don't catch that it is plural genitive. You could probably guess that "affirmavit" has something to with affirm, but you could miss that it is perfect tense. Of course, mentions of specific people and places are nearly the same.

Your person who speaks all four languages would have an easier time of it that an English speaker due to a high portion of cognates and a closer match of pronouns and some of the connectives like "qui" and "se".

It would not be a perfect comprehension, but I would expect them to pick up some of the message. I dunno, maybe 60%? More if they went to mass?