This page should help:
http://www.nmaoffroad.org/licensing.htm#dualsport
Essentially... you used to be able to, but now it's much harder, because the WSP wants assurance from the manufacturer that the bike meets FMVSS (federal motor vehicle safety standards) after you convert it... which is bullshit, especially with an older bike where the street models for that year would not have even met current standards.
"Sell" it to a friend in Oregon or Idaho, register/plate it there, and wait a while, and "sell" it back. WA dmv has to recognize registration from other states. That doesn't exempt you from the basic laws as outlined below, but it does mean that if it has a plate in another state, they have to honor it and let you register it here. This is how my Husqvarna 410 was plated, and it's a pure off road bike with a plate, a headlight and a tail light.... the PO did this in Idaho. This is also the way my TTR-225 was plated as well, that one was done in Oregon.
Make sure you have all the required equipment though when you ride in WA, because the cops do know the laws and they will bust you.
Headlight that is on while riding day or night
Tail light
Brake light that is actuated by at least the rear brake lever
License plate light
Turn signals
If they really want to be sticklers, they can probably get you on the following as well, but the cop that pulled me over did not mention any of these...
Dual beam (hi/low) headlight
Working horn
Speedometer/odometer (this one is fuzzy for me, since I think you are simply responsible for not speeding... if you're good at judging how fast is "too fast" without a speedo, then maybe you don't need it... the RCW's don't specifically state it's required anywhere, but when I went to register my TTR, they wanted an odometer reading... it didn't have one, so they put "000001" and then branded the title "NOT ACTUAL" for mileage).