Yes. Google Messages has a web version, and Spanbox's whole model is that if an app has a web app, you can add it. So you sign into Google Messages inside Spanbox exactly like in a browser and it sits in your unified inbox with the rest, your texts from Messages for web. It counts as one of your apps (3 free, unlimited on Pro).
You can even run more than one Google Messages account at once, each in its own isolated session, so a work and a personal Google Messages sit side by side without logging in and out.