No, there is no priority. The reason is that power "bus" on low-voltage side in MT devices is a very simple one and doesn't allow any preference.
There's a slight difference on devices which have DC inputs, on those power input with highest voltage is used. If power supply voltages (under load) are equal, then power will be drawn from both supplies.
I guess it's the same in your device, but you don't have control over internal workings of power supply.
Maybe you have other equipment and you can use an "automatic transfer switch" to switch between inverter and mains, and feed its output to the CCR2004 and maybe also to equipment that has only one powersupply.
Usually you can set a priority in such devices (or it is fixed and you can wire it according to your preferences).
We also use that behind our UPS to handle failure of the UPS while power is still available.
Maybe you have other equipment and you can use an "automatic transfer switch" to switch between inverter and mains, and feed its output to the CCR2004 and maybe also to equipment that has only one powersupply.
Usually you can set a priority in such devices (or it is fixed and you can wire it according to your preferences).
We also use that behind our UPS to handle failure of the UPS while power is still available.