The procedures to get married in WA is simple and can be done in about 4 days if the prospective spouses are willing to be married without taking the time to make elaborate wedding plans. The application for the marriage license does not have any question regarding whether a prospective spouse has an outstanding warrant. So, as long as the couple can manage to be married before the warrant is executed, the existence of the warrant should not be a legal barrier to marriage. (The couple may want to discuss the wisdom of being married when one spouse may be in jail or prison soon.)
The usual procedure to get married in WA is to apply for a marriage license, usually at the county's auditor office. The prospective spouses must sign the application certifying some things (such as they are both over 18, not related to each other, and have discussed with each other any sexually communicable diseases). The prospective spouses must wait at least 3 days before marrying each other.
After the 3-day period, the couple can marry each other anywhere within WA. Some courts have judges that officiate the wedding in court. Some private businesses have persons who can officiate a wedding.
The wedding must take place before some number of days have elapsed (I think 60 days).