No, Nier is part of FFXIV in the same way that FFXII and FF Tactics are part of FFXIV: it is not. Characters and events in FFXIV that resemble characters and events from Nier are not the characters and events from Nier. They are characters and events that resemble characters and events from Neir. In the same way, it's safe to say that characters and events in Nier that resemble characters and events from FFXIV are not the characters and events from FFXIV.
Until an XIV dev says, explicitly "the events in this other game that isn't FFXIV are canon to FFXIV" or the information appears in official FFXIV material, you cannot assume canonicity.