Here's a link to a long article [32 pages] about an observed Iron Sun.
http://www.arxiv.org/PS_cache/astro-ph/pdf...403/0403402.pdf
This star is a close binary 0.7 solar-mass companion to an 11 solar-mass black hole. The article guesses that the star was enveloped by the pre-supernova and spiraled in through the thin outer layers, and that the supernova happened before it coalesced into the core of the giant.
The article reports an Fe/H ratio of 0.14 +/- 0.12. Since Iron is substantially heavier than hydrogen, this means that much more of the mass of this star's atmosphere is Iron than is hydrogen.
I think this example shows that an Iron Sun is possible, but doesn't speak well for the likelyhood that our sun is one of these, as we don't have a large black hole orbiting our sun, and we don't have much iron in the sun's atmosphere.