Yes if power inverter or UPS supports that. Often power inverters made for supplying long backup to multiple household and office appliances are designed to complete circuit with input neutral as well. So in case you do not connect output neutral and just supply phase from output to required appliances and devices, the circuit should complete with input neutral if power cable of inverter or UPS is plugged into circuit board.
Before going for this, you should check whether your power inverter or UPS supports this kind of ‘phase only’ wiring. To test and confirm it, connect a bulb with output phase/live and input neutral while inverter or UPS is running on backup mode. If bulb glows it does support ‘phase only’ wiring. If it doesn’t then your power backup device is designed to completely isolate neutral when it shifts to backup mode. Go for complete wiring including both phase and neutral wires supplied to lights, fans and electronic devices. The other solution is to connect output neutral with a wire to mains or distribution board neutral. That will complete the circuit and you won’t need to wire neutral for every appliance or device you are going to connect with your power inverter or UPS.
This explains how common or non-isolated neutral of power inverter or UPS works. Input and Output neutrals always remain connected and only phase/live is switched over from power supply to backup mode with a relay.
In case of running multiple computers, servers and other sensitive electronic devices, go for complete wiring that is phase and neutral must be supplied from output. You may use extension cables for that purpose.