I recently had it confirmed to me by your support team in request #522074 that it is currently not possible to backup and restore the hardware mixer state of a Studio 1824c using Universal Control. The support rep responding to the case suggested that I may like to add a feature request for that in this forum.
I can see from other similar requests on this forum that Studio Live products have some ability to store mixer states in UC with scenes. While I would not expect to see a duplication of that product's functionality for the USB audio interfaces, having some ability to backup your mixer configuration to a file is not an unreasonable thing to want even on a consumer device.
Having already lost my mixer setup once, where a windows version update apparently caused everything to reset to the factory default state, I was disappointed to find there was currently no way of avoiding having to set everything back up by hand if this happened again in the future.