There is a lot of CO2 in atmosphere naturally, unrelated to human activity. If you remove all of it, then yes, most likely the Earth starts cooling and because the other important greenhouse gas – water vapor – has positive feedback, the cooling will go on till the Earth freezes.
That actually happened at least twice in the history of the planet – lookup « Snowball Earth ».
(No, it is not about ice ages, it was much more profound but much further back; before the time the live started supplying steady stream of CO2 into the atmosphere.)
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