Can a plane be IFR certified, but not allowed in IMC?
Question: Can these planes be certified for IFR, despite the IMC limitation?

No

Refer to  FAA Order 8700.1:


  B.  Type Certificate Data. Appropriate type certificate data will
  indicate whether the aircraft meets the requirements for IFR
  operations.
  
  (1) Section 91.9(a)prohibits aircraft operations without compliance
  with the operating limitations for that aircraft prescribed by the
  certificating authority.




if no, can they be used for training for one's instrument rating and for the instrument rating checkride?

Yes, as per FAA Order 8700.1:


  9.  USE OF AIRCRAFT NOT APPROVED FOR IFR OPERATIONS UNDER ITS TYPE CERTIFICATE FOR INSTRUMENT TRAINING AND/OR AIRMAN CERTIFICATION
  TESTING.  The following paragraphs are intended to clarify the use of
  an aircraft not approved for IFR operations under its type certificate
  for instrument flight training and/or airman certification testing.
  
  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.


For example, you can obtain an Instrument--Rotorcraft in an R44, even though its not legal in IMC.


  Although the R44 IFR Trainer was designed for instrument flight
  training, it is not approved for actual IFR operations. While student
  pilots are flying on instruments, the instructor must act as the
  safety pilot and operate only under VFR conditions.






if yes, then if one were to be flown into IMC, would be this be a legal violation or a warranty violation?

This would be a legal violation of 91.9(a)


  91.9(a) Except as provided in paragraph (d) of this section, no person may operate a civil aircraft without complying with the operating
  limitations specified in the approved Airplane or Rotorcraft Flight
  Manual, markings, and placards, or as otherwise prescribed by the
  certificating authority of the country of registry.