Is iCloud Mail available in Spanbox?

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

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