Where you have indicated doesnt look to have a buldge/flare for a thermostat to be in so it doesnt look like it should be there but if it does have a round buldge/flare then i guess thats where it could go. Check the other radiator hose and follow that to see if there is above mentioned flare thingy there.
As for radiator fan turning on if you dont have a thermostat then it will be always running colder than it should but the coolant will run hotter so im guessing that it could cause the fan to turn on more often than it should. Thermostat is designed to open and close depending on temp to keep head in desired operating range.
Btw this is a toyota forum
- LeeRoy
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