Will concrete harden although some rotted wood is still in hole?
Hydration is the chemical process by which concrete mixtures harden. Absent a retarding admixture, the hydration reaction occurs in any proper concrete mix. Wood, rotten or otherwise, is not typically a retarding admixture.
Embedding rotten wood in a foundation is not consistent with good practice, industry standards, and building codes. Furthermore, embedding wood in concrete is, in general, a sub-optimal practice.