If there are fridge and ac in same room. when ac is offed will the temperature inside fridge increa?

Here in this case you have kept your refrigerator open and so your room becomes a part of the refrigerator chamber or the evaporator and so you might think that the room will get cooled but the condenser is still within the room so the work input you are supplying to the compressor is discarded as heat in the condenser , since energy can't be cracked ,the work given to the compressor will be continuously rejected as heat in the condenser till the compressor is switched off.