Not here in Los Angeles. Here, Christmas/Theophany is always January 6, regardless of the day of the week. However, in areas of the US where the Armenian population is smaller, I have heard of it being moved to the nearest Sunday. It's improper, I guess, but the priest is being sensitive to the needs of his flock.
In the Los Angeles area, though, enough people can make it on January 6, that the rounding off is not necessary. In fact, I heard that the Glendale Unified School District even closes their schools on Jan. 6, because they know so many kids aren't going to come to school that day. (Glendale is a Los Angeles suburb with a large Armenian population.)
I think the Old Calendar Christmas was moved to the nearest Saturday to make it easier for the Jerusalem-Armenians to all make it.