Technically you can fly IFR without communication radio - from an uncontrolled field to an uncontrolled field with instrument approach without traversing controlled airspace. Get clearance before departure via phone - clearance limit time issued - the call upon landing to close flight plan...wouldn't advise it but it can be done legally - or at least it could last time I checked the FAR's (Federal Regulations) - I'm sure someone will correct me if that has been changed.
Very unusual, though.