Literature about a naive approach to graph isomorphism by inspecting polynomials of adjacency matrices
Yes, there is such a theorem, more or less. It basically states that the k-dimensional Weisfeiler-Lehman procedure subsumes (i.e. dominates) all known combinatorial approaches to graph isomorphism testing. (Your concrete proposal should be subsumed by the 2-dimensional Weisfeiler-Lehman procedure, if I am not mistaken.) For each fixed k, there is a class of counterexamples to the k-dimensional Weisfeiler-Lehman procedure known as the Cai-Fürer-Immmerman construction.

I first learned the basics of the Weisfeiler-Lehman procedure and the Cai-Fürer-Immmerman construction from


  http://users.cecs.anu.edu.au/~pascal/docs/thesis_pascal_schweitzer.pdf


There is much more to learn about the Weisfeiler-Lehman procedure than described there, but at least the treatment of the Cai-Fürer-Immmerman construction is complete and sufficient for your purpose. "The Weisfeiler-Lehman Procedure", by Vikraman Arvind is a recent brief essay meant as an invitation to the topic.

Perhaps the crucial point to take away from my answer is that if you would find a purely combinatorial isomorphism testing method (like the one describe in your question), which is not subsumed (i.e. dominated) by the k-dimensional Weisfeiler-Lehman procedure, then this would be a breakthrough by itself, independent of whether the method would be actually useful.