It was never formal in the sense of an agreement among clergy. The feeling that I get from the older people, though, is that they really didn't have a problem going wherever convenient after the Genocide if there was no Armenian parish around. I'm speaking of our grandparents' and even parents' generation. I think part of this was from an ignorance of the difference between our Church and others.
Of course what I have encountered could just be peculiar to my area and to the people that I know, and not representative of the whole.
This may have been more prevalent in smaller cities and communities when there were not yet churches. Yet in most major cities in what is now the Eastern Diocese, where the majority of Armenians settled in the years after the Genocide, there were already churches either shortly before or immediately after the Genocide. Same goes for California, where there were already parishes well before the Genocide. While there were isolated pockets of Armenian communities in smaller places, Armenian immigration tended to flock people together in very specific places.
Armenians were generally told to go to Episcopal parishes because Episcopalians reached out to not just Armenians, but Russian and other EO ethnic groups as well to provide space for worship. In some cities, this stretched even into the 1950s. And, for decades, much of the English-language Sunday School material in the Armenian Church in the United States came from the Episcopal Church. Thus, many Armenians developed a respect for the Episcopalians, and would defer to go there when there wasn't a church available. The trend seems to have turned in recent decades, and the Armenians I know who have moved to obscure places without a church usually go to a Greek or Antiochian parish. When I lived far away from a church for a while, I went to a variety of Russian parishes. Then again, I was raised both EO and OO, so it wasn't a stretch for me. I just didn't take communion.
As for one of the other side discussions, yes, many people went to other Protestant churches as well, and some Protestant traditions did attempt to "poach" Armenians. (Which, interestingly, was the impetus for the first Armenian Church in the United States when a Swedish Protestant minister in Worcester, MA attempted to do just that.) But once the Armenian parish opened (if there wasn't one), people generally went there. Please do not confuse Armenians going to Protestant churches with the Armenian Protestant/Evangelical/Congregational Churches, which is a different phenomenon.