Under the given description of what an alloy is, steel can not be regarded as such. I'll explain what category does steel fall under.
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Sites and references:
https://ehttps://en.wikipedia.org/wiki/Ferrite_(magnet)n.wikipedia.org/wiki/Ferrite_(iron)
https://en.wikipedia.org/wiki/Carbon
https://en.wikipedia.https://en.wikipedia.org/wiki/Ceramicorg/wiki/Cementite
https://en.wikipedia.org/wiki/Ceramic
https://en.wikipedia.org/wiki/Alloy
https://en.wikipedia.org/wiki/Steel
The Mössbauer spectroscopy of iron carbides : http://www.nature.com/articles/srep26184
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