Yes, though they can also ask for your lab results or to inspect your testing facility and hit you with massive fines if it turns out you falsified your compliance documents. As you mentioned this is very rare though - even enforcement actions against non-certified intentional radiators are uncommon.
I recall trying to build some hardware in 2020 and getting discouraged because of the CE/FCC silliness. Even though I could self declare for the EU it seemed like a big risk to do so.