Yes there are training's for District Committee members.
You might want to ask your District or Council Training Chair about the District Committee Training Workshop, the complete workshop plans can be found in: No.34160B.
This along with the NLE might be all the training that a District Committee member who is not interacting with youth members might need to be considered trained. All councils require YP for those committee members that would be dealing with youth members.
We have District Committee members that never see a youth member. Guys on the Finance Committee that only deal with the community campaign, they never have any dealings with our youth members, while the people who serve on the advancement committee might be dealing with youth members a lot and they defiantly require the YP training.
The BSA web site states:
All adult leaders must have completed BSA Youth Protection training before participating in any Scouting event or activity involving youth members.
Some councils require all adults to take the training while others only require it for leaders participating in events or activities that involve youth members.
The best thing to do is check with your District Training Chair
NE-Region Area 4 International Scouting Chairman.
Men of power are admired. Men of character are trusted.