There's no easy way of telling if there air in the system, symptoms may include erratic temp gauge readings or being higher or lower than normally, heater not as hot as normal, or blowing hot/cold. Given that the cap was off/ lost then there's every chance there air in your system.
The way the system works is that when the coolant heats up it expands, the excess expands into the header tank, when it cools down the excess is drawn back into the system. If the cap is off then instead off drawing coolant back in, it can draw in air.
When everything is normal the system will find it's own level, if the header tank is over filled when its cold then excess will be expelled out the overflow when the system heats up so finding its own level in the tank.
In your situation I certainly wouldn't take the chance, I'd bleed it as per the manual.
All 3 models of MR2 have great cooling systems IF they are properly maintained. The other thing all models have in common is they do not like being overheated

This pdf covers mk3 coolant replacement including bleeding
LINKY