There's nothing "genetic" about how MCMC works. AFAIK, usually with GP, you keep multiple candidates that you evolve together, which is not the case here (it's much closer to metaheuristics such as Simulated Annealing), e.g.:

  let candidate be some random program
  while candidate not correct (per your SMT solver):
      new_candidate = mutate candidate
      let cost be cost of new_candidate
         (varies by different techniques;
          some just measure the number of bits differ
          from expected output of testcases)
      if cost is improved:
         candidate = new_candidate
      else, with some probability (the lower the cost, the higher the prob.):
         candidate = new_candidate

Of course, there's nothing preventing you from using GP instead of MCMC to find programs. The focus of research is on how to mutate (e.g. how do you avoid generating bad candidates based on past experience) and evlaute the cost of a candidate, rather than the methaheuristics itself.