Can I use Fastmail in Spanbox?

Yes. Fastmail 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 Fastmail inside Spanbox exactly like in a browser and it sits in your unified inbox with the rest, your inbox. It counts as one of your apps (3 free, unlimited on Pro).

You can even run more than one Fastmail account at once, each in its own isolated session, so a work and a personal Fastmail sit side by side without logging in and out.