This is interesting. My name check is completed and evidently on the way back to USCIS.
Nonetheles, I contacted my Senator several weeks ago and received the standard letter from his staff. However, what was interesting was an attachment by the Senator's office staff called "USCIS CASE STUCK IN FBI PULGATORY?". Certain passages were highlighted, in particular the criteria for the expedite name check (which evidently still exists). One staff member highlighted as one of the five criteria:
"Writ of Mandamus - lawsuit pending in Federal Court." So it seems that, as U.S. Congressmen and Senators cannot according to the FAQ National Name Check Program pamphlet, which was laso attached to the letter from both my Senator and the Congressman ("Because each customer agency determines which name checks are expedited contatcting Congressional representatives, the FBI's Office of Congressional Affairs, or the NNCP will only further tie up vital resources and will not contribute to the expediting of a name check.") expedite the case, Congressional representatives (or their staff) list the lawsuits as an opprotunity.
However, I believe when you write the WoM it is helpful to list that you were active in the attempt to get the matter resolved (letter to the Congressional representatives etc) even though the outcome is questionable.
I thought it was very interesting receiving a letter from a U.S. Senator that clearly and explicitky indicates the lawsuit as a way to expedite the name check.