I deal with a similar system at my work and it works pretty well.
We basically have a global box and that gets added to everyone’s Outlook. That global box collects all the emails. You would have to add the global box to everyone’s outlook so it would be a subset of their regular inbox It acts like a queue and you can see which emails have been read, responded to etc (by the default Outlook way.. Bold, Not bold etc).
The only thing is that you wouldn’t be able to see is, who responded, but that can be done by CC that global box but someone would have to sort that into a sub folder.
Also, when you reply, you have the option of choosing who the sender is as well.
Hope that helps and makes sense.