In theory, if I can run it in FireFox, there should be no problem. Of course the devil is in the details. Has anyone tried this?
I have an Office 365 license for work, and it does indeed work from a Linux machine. (I didn't get the license by choice >.>)
The only difference is that if it's an Office for Business you have to go through your workplace's Sharepoint namespace rather than the office.com online versions; however it will still function as normal.
Office 365 runs on my Ubuntu 18.04 via Firefox. Have 365 at work and can send & receive messages at home. Can also load & run Word & Excel at home. Not 100% functional but is doable. If you do not have access to 365, you would need to register with 365 and pay a fee to use it. It should still work with Linux & Firefox.