Both Washington and California are members of the driver license interstate compact which means that they share information on suspensions due to criminal convictions. Washington will require you to resolve the problems in CA before issuing you a license.
The quick answer is no. WA Department of LIcensing will not issue a driver's license to you until you have resolved the revocation in CA. You should immediately contact CA's DMV and ask them how to resolve the revocation down there. Only after that revocation is resolved with WA issue a license to you
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