DACE is actually ACED, and would be named for the minor third interval, which makes it an . To be a chord, you have to have a triad, and you have to have an interval of either major or minor third voiced--your suspended 4th is not,in musical nomenclature, a chord(sorry to disappoint so many of you)--in classical music theory, the 4th is regarded as a non-harmonic note that is suspended, or lingers, from the previous measure--it is a variant of the appoggiaturra. This is handy for your student to understand, because, in that DADGAD scheme, there is a lot non-harmonic stuff happening--

Pop and Folk Guitarists(as opposed to classical guitarists) tend to view chords as the basis for a musical piece, so the idea of there not being a chord somewhere is a conceptual problem for them--but there are a lot of times when you don't have a chord happening--also many of the note configurations that guitarists play are misnamed, because the notes that are sounded delete or substitute notes, either because it is awkward to play them, or because it sounds better when they are deleted (Fifths, especially in lower registers are often deleted for this reason), so when you learn the to play the little dot pattern above the music staff, and you memorize the name of it, you have not infrequently been duped by a hack arranger--