I'm a procedural approach (without radar) and tower controller.
If an IFR aircraft is VMC I would orbit no problem, if the weather was dodgy I'd say "orbit mantaining own terrain separation, or go around"
If the aircraft is IMC I wouldn't allow an orbit unless the pilot initiated the request and agreed to mantain their own terrain separation. In this case I would suggest a missed approach would be the safer option.
However, if you have radar I imagine it would be fine to approve an orbit, subject to the RMAC (radar minimum levels chart). Perhaps you would say "Orbit approved, not below 1000' until re-established on the ILS". I don't have a ticket though, so don't count me on this!