Well, this question is open to interpretation. The literary purpose for those letters was to provide an outer frame for Shelley's novel Frankenstein. The character of Robert Walton provides both an audience and validity for Victor Frankenstein's story. The letters to his sister provide information about Robert before we meet Victor and show us the parallels in their character.
This being said, there is no real literary reason the letters would have to be received by Mrs. Saville as she is essentially a VERY MINOR character. She does ever enter the story again. However, there is no reason they would not be delivered. The letters would have traveled from boat to boat and port to port, so certainly the timing of their delivery would be uncertain. Some letters may be lost; some may arrive out of order. The idea that Robert is wanting to share his experiences is important, so I would like to assume that his attempt was successful.