I don't see any problem with it whatsoever. I may be speaking a personal judgment, but I just can't see any problems with the authenticity of the documentation supplied by the funeral director. I hope Service Canada can enshrine the legitimacy of the process as well. If it requires some provincial, official documentation, that just delays the process. I would leave it in the hands of the professionals to work it out.
The short answer to your question is that there should not be a problem with it because copies of the documentation are normally accepted by the various departments and any other interested organizations.