It is possible, the EPS output from a Deye inverter can supply your whole house if you want, not only the essential consumers.
It can supply up to the limit of the inverter (in your case 10KW) from PV and/or battery and if you don't have enough power from PV and or battery then it will take the missing part from the grid through Deye's grid connector (grid-assist).
You will not even need a CT if you run everything on the EPS output, there is a setting for it:
"Zero Export To Load: Hybrid inverter will only provide power to the backup load connected. The hybrid inverter will neither provide power to the home load nor sell power to grid. The built-in CT will detect power flowing back to the grid and will reduce the power of the inverter only to supply the local load and charge the battery."