what computer will you be running? standard ECU's use the O2 sensor to tell how much fuel is going into the engine and being burned. without this sensor your computer will not sense this and prob think that there is not enough fuel resulting in a rich fuel mixture, or it might just go into limp mode, and barely run the engine at all.
i have seen a 86 run well without one, but his had a microtech ECU. the car ran fine and went well (had a 20V) but used the fuel to do it. whe i re wired his computer we fitted an O2 sensor and wired it up hoping that this might reduce fuel consumption. i cant say if this worked because the car is not yet on the road, (See craigs AE86 project in members cars).