If you have an official AC adapter, or at least one with the same rating as the original, your Neo Geo should be just fine. When using a AC100 adapter in a US AC120 power socket, the only risk is damaging the AC adapter. It'll still output it's rated power, but the internal components might see more wear with that 10 - 20 AC difference.
Personally, it's a bit paranoid to unplug the Japanese power supply just because it's slightly below US power socket rating, but then people sometimes do it even for US power supplies. Basically, the difference between 100 and 110 - 120v AC is negligible, but it's not necessarily a bad idea to unplug your power supplies. They are constantly trickling a tiny amount of power from the wall socket. If you are concerned about the lifespan of your power supplies or you have to manage your power bill strictly, consider getting power bars you can turn off and leave them in easy reach. I might do it myself, maybe during the night.