From Frank Purcell of St Michael’s Russian Catholic Church via blog member Dave McLaughlin
Catherine de Hueck Doherty and info on how Eastern Orthodoxy canonizes saints (permanent link as PDF)
I think a lot of the late baroness and Friendship and Madonna Houses (Catholic Action/lay apostolates Vatican II all but killed); she is a fascinating person whose biography, They Called Her the Baroness, I've read and is a source of info for some of the following comments.

Because Catherine was reared in both the Orthodox and [Roman] Catholic traditions

Uh, no. She was Russian and a born Orthodox, but as the book and my acquaintance Archimandrite Serge (Keleher), who knew the baroness, have explained, she had a habit of exaggerating and even fibbing if she thought it helped her cause. Sadly, when she began Friendship House and later Madonna House, many RCs probably were wary if not hostile to the Orthodox tradition (witness the hostility of the Irish-American bishops to Slavic Byzantine Catholic immigrants). So Catherine concocted a story that her family, the Kolyshchkins, were Polish Roman Catholics all along. No, they belonged to the Church of Russia. Her mother was fascinating - an ethnic German and I think formally listed as a Lutheran, like the German born-Lutheran empress of Russia she enthusiastically practised the folk religion of the Russian Orthodox, going on pilgrimages (паломничества), etc.

Would the canonization, in the [Roman] Catholic Church, of someone from Orthodox Russia (that is, Catherine), be an obstacle of any kind to Orthodox Russia’s openness to her gifts?

Honestly, yes, it might.

In her deep heart, Catherine belonged to both the Orthodox and [Roman] Catholic traditions.

Doubtless true of another favourite, Archimandrite Lev (Gillet), whose pen name was 'A Monk of the Eastern Church', but again, regarding the baroness...

She did help Russian Orthodox exiles in Toronto in the 1920s where she was instrumental in a moving example of real Catholic ecumenism back before such gestures were cheapened by indifferentism with Protestants - the RC archdiocese helped the Russians build an Orthodox church and priest's apartment and the archbishop even gave the Orthodox priest a chalice to celebrate the Holy Mysteries. She's one of those people who according to RC canon law should have been a Russian Catholic but wasn't: the fact is after her change of churches she distanced herself from that tradition most of the rest of her life, being somewhat afraid of it because of the aforementioned hostility. It was her friend now-Archbishop Joseph (Raya) of the Melkite Church, who lives at Madonna House today, who somewhat changed her mind about that in the later years of her life. (Photo: the baroness in the last stage of her life. The Russian pilgrim's clothes look like an Orthodox nun's habit except the nun's hat is taller.)

(But to give her credit, her own book Not Without Parables has some good stories from that tradition.)

It is certainly the desire of Madonna House that we also, “in our deep heart,” embrace our Orthodox brothers and sisters.

Of course that's wonderful and in as much as it's true I think one can thank the Melkite archbishop.

Anyway, in short how it works in Eastern Orthodoxy is a national Church (or its equivalent like the Russian Church Abroad) canonizes its own saints who are then recognized by all Orthodox.

The ancient saying in Orthodox/Catholic relations, that “our divisions do not reach all the way to heaven,” has been achieved in the saints.

Actually the recently canonized (by the Russian Orthodox in France) St Maria Skobtsova said that.

P.S. I take some credit for the disclaimer in the box at the top of St Michael's mission-statement page - I tipped them off about the rumour being spread years ago by some malefactor online that it was a gay church.