UTF-16 is not officially supported, but theoretically it should work because Javascript is UTF-16 internally. Saving the files in UTF-16 would likely break (but this shouldn’t affect you), but JSON.parse() probably correctly handles it, especially if the stream you use has the byte order mark (BOM) correctly specified at the beginning of the data.
Please test it, if it works, you are good, if not, let us know as I would like to communicate to others that it isn't supported.