By going this route your specific group may lose control, which is the whole idea behind becoming 501(C)3. If the district is the official non-profit they may be able to use your hard earned funds for whatever they want, elect or control your Executives, decide what your group will do, etc. Having a district group for brainstorming is great, but keep control within your own group.
Overall it doesn't cost that much to become independant and the benefits are well worth it.
The PTO Leaders in our school district have begun meeting monthly to brainstorm and share ideas and concerns. Our district currently has 9 elementary schools, 2 intermediate, 2 middle, and 2 HS campuses. Only one PTO is actually a 501(c)(3) group.
Most are interested in becoming 501(c)(3) and some of us wonder about the possiblity of forming an umbrella group for the district. Is it possible to allow all participating groups to basically remain financially and operationally independant, yet report under 1 tax id number?