Yes
If your registration has not expired, you must turn in your plates. A driver's license is suspended when the lapse is 91 days or more or if the lapse time period has not yet been determined.
Can someone else register the vehicle?
The DMV will not issue a record to any person unless that person makes an affidavit on Form FS-2. The statement certifies that the purpose of the application is not to avoid the results of the current suspension. The local DMV office determines if the request will be accepted or rejected.