Yes. Mastodon 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 Mastodon inside Spanbox exactly like in a browser and it sits in your unified inbox with the rest, your timeline and DMs. It counts as one of your apps (3 free, unlimited on Pro).
You can even run more than one Mastodon account at once, each in its own isolated session, so a work and a personal Mastodon sit side by side without logging in and out.