Singular entity, plural name/nickname -- verb form?
The singular use of archives is quite grammatical in that it is in use by a respectable organization, and that a distinction may be made between it and the singular archive as noted by a commenter on this Language Log post:
This problem crops up with the technical use of "an archives." Among librarians, archivists and historians, the term "an archives" refers specifically to the repository in which papers are housed, not generally to the papers themselves. "An archive" means a single set of papers: "An archive of committee papers." There is some drift between uses and I imagine the singular "archives" will eventually fall out of use altogether, especially as copy editors and people like that are always trying to correct it.
This corresponds to the National Archives' own definition:
An archives is a place where people can go to gather firsthand facts, data, and evidence from letters, reports, notes, memos, photographs, and other primary sources.
The above mentioned Language Log post itself concerned the similar case of a chambers meaning a law practice, three instances of which may be found in the Hansard Corpus (British Parliament).
The Terrell plan has been advocated for some years now: It has been revived again by Mr: Edward Terrell, who is a Queen's Counsel, Recorder of Newbury, 1473 author of a book on running-down cases, and is, I gather, head of a chambers which has great experience of motoring cases of all kinds (Mr Roger Cooke, 1966)
Lord Gifford My Lords, for the past 15 years I have had the honour to be head of a chambers of barristers, which is unusual in two respects which are relevant to this debate (1989)
I come from a chambers that specialises partly in competition law (Sir Nicholas Lyell, 1998)
Does it matter that the full name of the agency is the National Archives and Records Administration?
Yes. The subject is that particular administration, and that would make it singular, even if you abbreviated it.
If, however, you were talking about the actual, physical National Archives in Washington DC, (which NARA administers :) ), then you are talking about a plural subject.