The OpenFlexure server does not require an internet connection. However there can be some issues with different computers which get very confused when there is a network connection which has no internet. I don’t use a mac, I think that I did try briefly on someone else’s mac and there was something that was an issue but it was not clear whether this was the mac or the ethernet dongle.
On Windows I regularly connect with no internet, using an ethernet cable and a USB-Ethernet dongle. To do this the computer and the Pi have to work out an ad-hoc network, and I think this is where sometimes it does not work. I find that there are some dongles which do not work with some computers, and I expect that Mac will deal with ad-hoc networks differently from Windows.
@j.stirling uses a small travel router which might work better in your situation. Again there is no internet connection to the router, but I think the router will take charge of the network. He did have some problems with Android devices which dropped connection to the microscope network as soon as they realised that there was no internet connection and went searching for other local networks instead.