Would those churches recognize converts received into another jurisdiction by chrismation as being Orthodox?
Depends on what you mean by "churches."
I am unaware of any synod of Bishops (outside of some Old Calendarist synods that have intentionally separated themselves from "World Orthodoxy") that refuses to recognize converts received into another jurisdiction by chrismation. For example, it is not unheard of in some parts of the Church of Greece to baptize converts from many Protestant confessions. However, the Church of Greece does not refuse to recognize or retroactively baptize those who were received in some other way. Such is also the case in canonical Orthodox Churches that follow the Old Calendar (e.g. ROCOR, Jerusalem, Russia, etc.).
That's one understanding of "church" -- official policy, so to speak. However, a certain Bishop or priest may decide to do his own thing in a specific location. This is rare, and, in my experience, happens more frequently in either (1) an Athonite context, or (2) in areas of the diaspora that have less ecclesial organization than North America (e.g. Brazil or Austria or New Zealand).