Homomorphic encryption (HE) is a privacy-preserving technique that enables computation directly over ciphertext. Unfortunately, a key challenge for HE is that implementations can be impractically slow and have limits on computation that can be efficiently implemented. For instance, in Boolean constructions of HE like TFHE, arithmetic operations need to be decomposed into constituent elementary logic gates to implement so performance depends on logical circuit depth. For even heavily quantized fixed-point arithmetic operations, these HE circuit implementations can be slow. This paper explores the merit of using stochastic computing (SC) encodings to reduce the logical depth required for HE computation to enable more efficient implementations. Contrary to computation in the plaintext space where many efficient hardware implementations are available, HE provides support for only a limited number of primitive operators and their performance may not directly correlate to their plaintext performance. Our results show that by layering SC encodings on top of TFHE, we observe similar challenges and limitations that SC faces in the plaintext space. Additional breakthroughs would require more support from the HE libraries to make SC with HE a viable solution.