It's possible it will happen - it's possible it won't. What we have seen in the last couple of years is that INZ have been shifting cases around to different offices to wherever officials have some spare capacity. (This started after the Christchurch rebuild meant there was a huge rush of applications, so they were getting snowed under at a time when they already had the difficulty of relocating after the earthquake.) Some applications from people already in NZ were even dealt with by London.
So all we can say for certain is that, though you have to put in your application to the nearest INZ office, it may end up being dealt with somewhere different. And while previously, your case would have been moved when you did, now, it might not be.