VOR requires valid heading to show a valid bearing on a RMI, for the deviation bar to work against a pre set course a valid heading is also required.
ADF does not REQUIRE a valid heading to indicate correctly as it always indicates relative bearing, however, conventionally, this is usually in a RMI or HSI presentation which of course needs a heading input.
My (engineering) opinion is that you wold be up the proverbial creek wihout a paddle and vectors for visual on stby instruments with perhaps a little assistance from the NDBs is the only solution.