It's certainly possible but it's also unlikely because of a chemical property called Valency. Put simply, carbon makes a great basis for organic compounds because it's naturally tetravalent, or in other words can combine with 4 other elements or atoms to form new molecules. This means that you can quickly build very complex molecules with substantially different properties from each other, just sticking with a few common elements.
CHNO (Carbon, Hydrogen, Nitrogen, Oxygen) compounds are the basis of complex life on Earth and from these we get carbohydrates, LSD, alcohol, caffeine, morphine, and many other types of compounds that when used within a complex lifeform, have massively different effects.
Iron is at best trivalent, as I understand it usually bivalent, meaning it doesn't quite have the same ability to build complex organic molecules as carbon. If it could, we'd probably be iron based life forms because iron is more plentiful in our environment than carbon is.
Also, because iron oxidises VERY well, it may well restrict the capacity of the lifeforms to metabolise and oxidise because any oxygen that comes near the iron in the lifeform is likely to be trapped exceedingly well. This is in fact how our hemoglobin works to get oxygen through our bodies right now. If the entire lifeform was iron based, it may not be as efficient at getting oxygen to all parts of it.
This is one of the key reasons why silicon is generally seen as the most likely candidate for alternative biochemistry, although it's not as prevalent as carbon. Another possibility might be Chromium (because in certain conditions it can be hexavalent), but that would be even more exotic a lifeform to form and it is difficult to imagine how it might work.
So possible? Yes. Practically possible? Probably not, at least not if you want complex diverse life on your planet.