In general yes. In this specific case not entirely, because once the radiating nucleus has undergone positron emission it has turned one of its protons into a n

In general yes. In this specific case not entirely, because once the radiating nucleus has undergone positron emission it has turned one of its protons into a neutron, which means it now needs one less electron in order to form a neutral atom. The "spare" electron can wander off and replace (eventually, on average) the electron that gets annihilated by the positron.