Michael,

Yes, the third note is really there, and is called a combination tone-- and it does happen with other instruments-- the great composer and music theoretician, Paul Hindemith, explains how they work in his "Craft of Musical Composition", and presents it in a way that is practical for writers and arrangers--

The guitar is particularly prone to producing good combination tones, which is why the partially voiced chords often work--a trick for getting good combination tones is to have a spread of an octave or more between tones in the interval--

Whether it is a chord or not depends on which notes you play--for some intervals, fifths and forths, the tone is an octave or two below of one of the pitches played--however, when you play the interval E-C on the Treble staff, the G below C sounds (although it is not necessarily loud enough for you to consciously hear) and, if you choose to think of it that way, a chord is sounding--