Not yet, and the honest reason is KakaoTalk has no official web app, so there's nothing for Spanbox to run locally (Spanbox loads each app's web version on your machine). It's on the roadmap for if and when KakaoTalk ships a web client, it's in the same boat as Signal, Viber, LINE and KakaoTalk. For now you'd keep using the KakaoTalk app itself.