Locally implies an email server on every machine. While technically possible, it would be an abysmal situation with constant problems.

Hosting your own in network would be much more feasible. You’d likely have some annoyance but beyond that it would work.

Of course you have to ask yourself why they would bother when a large portion goes through outlook servers anyway, and the majority of the other portion goes through Google servers. You’d have to do a cost vs benefit analysis to know for sure, especially if you don’t have anyone on staff that can handle the task.