Perhaps this is off-base relative to the answer that an EO person would give (and I did purposely start this thread on your board, so feel free to correct as necessary, EO people), but I would think that if a Western saint were to be added to an Orthodox church's calendar, it might not be a matter of when, but of why. Like in the case of the chronologically latest saint shared by OO and EO, St. Isaac of Nineveh (fl. 7th century), he became very influential via monasticism due to the popularity of his ascetical homilies, and so it makes sense that OO and EO, both very much steeped in monasticism, would recognize him. It's not so much about the time or place that he was born, because there are plenty of other people from the same background (Eastern Arabia) and time period that are not recognized by either communion, such as Gabriel of Qatar, Dadisho Qatraye, and others who are of the Nestorian confession (their "Church of the East" was big in the region at that time). Of course nobody who venerates him (except for the Nestorians themselves, of course) believes that he actually was a Nestorian (theologically speaking), as there is a distinct lack of that viewpoint in his homilies (at least the ones that I have read; I have had some Nestorian acquaintances claim that they are "scrubbed" in their translations, but I don't buy that, as the Syriac Orthodox still venerate him, and they don't have to read him in translation).
I'm not sure under what similar circumstances a distinctly post-Great Schism Western saint might be popular among the EO, especially if you consider that by the time of St. Isaac's death, the Nestorians had been out of communion as a Church not just for a bit (so it's not like these guys who died in 1068 or whatever), but for several centuries.
To the extent that I have had it happen both here and in real life with EO friends that they did not know that some of our modern desert fathers were actually "ours" and not "theirs" (that is to say, OO and not EO), I could actually see something like that happening in the future between OO and EO with regard to, e.g., Fr. Matta el Meskeen/Matthew the Poor (I don't know that he is technically a saint yet, as he only died in 2006, but he is certainly already popularly thought of like that by many Copts, and that's kinda how the ball gets rolling in Eastern/Oriental Christianity). Who in the modern Western church is recommended by those not even of that communion, to be published by their publishing houses (as the English translation of his Orthodox Prayer Life was, and a few others), etc., as in this case? I'm not going to say it wouldn't happen, but I don't have a ready example of someone who might occupy that space, which is probably fairly instructive in itself.
If there were/is such a person, however, then of course they could come from anywhere and any time. While it's not exactly the same as the point I'm making, it is worth thinking about how we (the Coptic Orthodox Church) have already added the New Martyrs of Libya to our syanxarium (February 15/Amshir 8), and hence publicly venerate not only our own Coptic Orthodox people, but also one person who was not even any kind of Orthodox (the Ghanaian Matthew Ayariga, who some say was not even a Christian originally), because when pressed, he reportedly said "their (the Coptic Christians') God is my God", and hence was executed along with the Copts.
Even if some combination of factors might make it more or less likely that a saint may be found here or there (in the sense that it's not a mistake or an oversight that there aren't any recognized Orthodox saints among the population of Vatican City, by the very nature of the place), it's ultimately not a matter of background, culture, time period, or any of this stuff. It is a matter of faith.