Can a 2.2 engine run without a thermostsat in a outback?

why do you want to. This would be a terrible idea as the 2.2 engines have head gasket issues. When the gasket weakens, the engine will start to overheat, and without a thermostat you wont know until the gasket blows and you ruin the entire engine. So you "can" run without a thermostat if you feel like blowing your engine.