Would a Sukkah that has walls that are completely transparent be kosher for use?
Yes. The first mishna of Maseches Sukkah lists the different factors that would invalidate a sukkah, but transparency isn't an issue. You can also make the walls with 4 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.
In Maseches Sukkah 4b (copied below), Rava rejects Abaye's proposal for a platform without walls because there is a requirement that they be "ניכר". Therefore there may be a basis for transparent walls being invalid.
היתה גבוהה מעשרים אמה ובנה בה עמוד שהוא גבוה עשרה טפחים ויש בו הכשר סוכה סבר אביי למימר גוד אסיק מחיצתא א"ל רבא בעינן מחיצות הניכרות וליכא
Rabbi Yoshia (Sukkah 7b) claims that walls must also provide shade and therefore may not be constructed from transparent material.
But I think you can decorate the walls enough to guarantee enough shade for comfort or lay plastic sheets like tarp. Since I am a female, I am not a posek, but just suggesting my idea to help solve the problem of a sukkah with transparent walls.
The Pri Megadim is מסופק about this case.