Would a Sukkah that has walls that are completely transparent be kosher for use?
Yes. The gemara in the beginning of Sukkah discusses different factors that would invalidate a sukkah, but transparency isn't an issue. You can also make the walls with 3 horizontal strings, each within 3 tefachim from the other one. Though if it was completely transparent, i.e. invisible, perhaps there would be an issue that no one could tell they're in a sukkah.