The short answer is no. Loss of license typically disaalows use of all mechanized transportation devices. Registration with the MVD is not the criteria in which the analysis is done (although I agree it should be).
If your driving privilege is suspended for DUI, you cannot drive a motor vehicle. Under California Vehicle Code 415(a), that means "any vehicle that is self-propelled." There is an exception for self-propelled wheelchairs and tricycles operated by disabled people.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like Avvo, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
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