Not sure...I didn't end up buying the 30 pin cord or adapter or try their onboard cord (at that time, the 30-to-lightning adapter was only available through apple directly at a really high price).
I do know that a lot of adapters (e.g. Micro USB to Lightning etc.) have connectivity issues for some applications, even if they are MFI.
But from a simple hard connection standpoint it might just work...