The ambient temperature is the temperature of space surrounding the component. It doesn't enforce a temperature condition at any surface. Once you apply any BC to your model, say temperature, this will govern the behavior and the ambient temperature will only be used to calculate convective heat transfer.
In order to control the convective heat transfer, you can set a 0 convection coefficient. This would mean no heat transfer using default BC, but any other convection BC applied to this surface would still act and this approach does NOT enforce any adiabatic condition.
In a nutshell, zero convection coefficient only suppresses the default BC (as good as deleting the BC altogether) and the ambient temperature (which is used to calculate heat transfer) doesnt play any further role. So even if there are faces you see assigned to ambient temperature, it shouldn't be a problem since the faces are not forcefully assigned this temperature. Further, a zero coefficient does ensure no heat transfer through this surface using default BC.
I hope that answers your query.