Although I think most people are correct in that the Septims are only Dragonborn symbolically, I do think Martin Septim was an actual Dragonborn in the same sense that the Dovahkiin is. He morphed into a Dragon for Christs sake. He was not just another normal Septim.
I agree with this, and also enjoyed the post!
Presumably not just anyone can turn into an avatar of Akatosh - for instance, I'm not 100% sure I could (but on balance I think I could probably could)
Whether or not that means he could do the shouts and the rest, not sure. Certainly Tiber Septim/Talos must have been able to seeing as the Greybeards got excited enough to beat one out (I mean a call from the top of the mountain, you sickos) when he turned up