Parking tickets do not get reported on your driving abstract or criminal history and would not affect a deferral. HOWEVER, I would be hesitant to pay a parking ticket issued as a traffic ticket until I was clear that the officer did not make any other mistakes such as putting the wrong infraction number on the ticket. Consult a ticket lawyer before paying the fine.
The notice of infraction for a parking citation often will indicate it is a traffic infraction however this does not necessarily mean that the finding that you committed the infraction will end up on your DOL record.
RCW 46.20.270(2) provides that a court shall immediately notify DOL when "any person has committed a traffic infraction in said court for a violation of any said laws other than regulations governing standing, stopping, parking, and pedestrian offenses".
That being said each judge is allowed to craft their orders for deferred findings. You should review the order on deferred finding and as the other attorney indicated it is always good to contact an attorney who handles infraction matters. If you do so, I recommend you have a copy of your citation handy.