Is okay to use the Great Seal of The United States for Non-Commercial use?
The various seals of the United States Government aren't governed by copyright but by 18 U.S. Code § 713. Section a covers the great seal of the United States (emphasis mine):
Whoever knowingly displays any printed or other likeness of the great seal of the United States, or of the seals of the President or the Vice President of the United States, or the seal of the United States Senate, or the seal of the United States House of Representatives, or the seal of the United States Congress, or any facsimile thereof, in, or in connection with, any advertisement, poster, circular, book, pamphlet, or other publication, public meeting, play, motion picture, telecast, or other production, or on any building, monument, or stationery, for the purpose of conveying, or in a manner reasonably calculated to convey, a false impression of sponsorship or approval by the Government of the United States or by any department, agency, or instrumentality thereof, shall be fined under this title or imprisoned not more than six months, or both.
Based on a plain reading of the law, it would seem that you are allowed to reproduce the seal so long as you do not do it in such a way that would convey approval by the government to do so. If you actually intend to do this, you may consider checking with a competent attorney to make sure your use does not "convey a false impression of sponsorship." Note that this only applies to the great seal, the rest of the section covers the seals of the President, Vice President and the houses of Congress and specifically requires approval by an appropriate entity before reproduction of those seals, depending on the context.