Come to think of it, it doesn't even need to have all the Equiptment operative to fly under IFR, you just cannot enter IMC.
From the FSIMS document :
A. IFR Training in Visual Meteorological Conditions (VMC). Instrument flight training may be conducted during VMC in any aircraft that meets the equipment requirements of part 91, §§ 91.109, 91.205, and, for an airplane operated in controlled airspace under the IFR system, §§ 91.411 and 91.413. An aircraft may be operated on an IFR flight plan under IFR in VMC, provided the PIC is properly certificated to operate the aircraft under IFR. However, if the aircraft is not approved for IFR operations under its type certificate, or if the appropriate instruments and equipment are not installed or are not operative, operations in Instrument Meteorological Conditions (IMC) are prohibited. The PIC of such an aircraft must cancel the IFR flight plan in use and avoid flight into IMC.