I think you can but people go wrong when they plug the memory saver into the obd and then accidentally let the crocodile clips touch each other.
Update: After trying it myself, it didn't work.
I used this bluepoint one:
I connected it to the obd port and used a small 12v battery as the power source. I removed the main car battery and charged it up in the house for 4 hours. When I put the main car battery back in and removed the memory saver device, my ECU had reset itself, meaning no power was getting through the OBD port. I used a multi meter to check if power was getting to the OBD pins on the OBD plug and sure enough it was, 12volts on pin 16 and negative on pins 4 and 5. One thing though, the instructions said plug the OBD plug in first and the yellow light should come on, but it didn't. The bluepoint one has a fuse, which I checked and is fine. I guess the yellow light comes on if there is power from the main car battery. In my case, no light means no power on pin 16 of the micra's OBD socket. I also checked the pins on the car's obd socket, no power on pin 16, or maybe I'm doing something wrong.
UPDATE: Just found out, in the fuse box inside the car, there's an extended storage switch which must be pushed in for the OBD socket to have power.