Yes, but that could change. The hardware itself would certainly be capable. And a POS system can also be cloud based, although not ideal. For hotels, these systems are already cloud based, but then the display is a bit small instead.

Last I read you don’t even get an App Store (!) to install third-party apps on the device, so I’m not sure if that’s possible.

It doesn't have its own app store. It runs the apps on your phone, so feel free to add any of the 2,000,000+ apps on the iPhone App Store to it.