Are Open Strings a Chord?
Yes. The definition of a chord is anything that is two notes or more. If you played the open strings E and A, you would be playing a chord. The chord could be an E sus, A5, or some color tones of another chord that has no root.
Many styles of music use open strings, in fact it determines the key signature many times. Writing a song in the Key of G# makes it difficult to utilize the open strings (unless of course you have a capo).
Keep in mind that if I play three notes and all three notes are the pitch ‘A’, then it is NOT a chord. A chord has to be two different notes.