The RFO (Responsible Financial Officer) is often a role that is carried out by the council clerk. So, yes, the RFO is frequently not a councillor. It can be any suitable person.
It is a function that must be fulfilled for a council to operate properly, so a council that has any financial transactions will need to appoint someone as RFO.
If the RFO is not a councillor, they may receive remuneration or may act voluntarily. A councillor acting as RFO may not be paid (and cannot be a paid officer for 12 months after ceasing to be a councillor).