Not likely Omen. The only ports that the GCN has left are a smaller one on the side, and the memory card slots. I am not sure what the bandwidth is like on the memory card reader, but I am thinking it's pretty low. The last remaining port on the underside is a little small for putting a hard drive in I think, and I once again think it's a little slow to be reading a hard drive.
But the big thing here is that adding a hard drive would really serve no point. There's nothing special about a hard drive. The GCN memory cards are plenty big enough, in spite of all the whining about them, and if Nintendo really needed the extra space for caching large amounts of data, (such as Earthbound DD), there's always the SD card reader.