Can I edit an office document in real-time with another person using Box?

Yes.  This is a feature Box/Microsoft released in early 2016.  You have to have a folder which you've shared with other collaborations.  Any office document in that folder can be edited simultaneously by two or more people.    Whenever you view a document, you'll first get a preview of that document.  To edit it simultaneously, you have to use the ONLINE Word/Excel/Powerpoint method of editing a document. 

Once you do this, you'll see the names of all the people editing the document and you'll see where their cursor is. 

While editing a document (initiated from the web interface), it will "lock it" to prevent others from editing a copy (unless two people go in via the ONLINE method).