No, it cannot be transfered.
Unfourtunately, Spiky-Eared Pichu, not only is stuck as a Pichu, but cannot be moved into Pokemon Home, and is stuck in HeartGold/SoulSilver. Therefore, we don't really know what Spiky Eared Pichu would look like. However, as shiny Pokemon show up as shiny, I would assume that the spiky ear would show up (although we can't really know, just a guess).
Hope I helped! :D