If you restore the NAND backup in the source system, Fieldrunners will be there, of course. However, a System Transfer won't transfer it anymore, since on Nintendo servers it isn't linked to your source console anymore, but to the target console. So, it's the same as if you had installed it via CIA or other non official methods.
OK no worries ... I'll delete it or restore the pre-fieldrunners NAND and purchase again.











