Compared to some around here, I'm a little flat in the theory department. I still feel the following is true and pertinent.

As a fiddler, two notes are the most I can play at any time. I tend to use 1-3 for major chords and 1-5 for minor - not all the time, but MOST of the time. The specific chord will be implied by the context of the song, but will be left to the listener's ear to fill in.

Some folks will hear the missing note as something you didn't expect. In a group playing situation, experienced musicians will adjust to this or adjust those around them. Often the loudest person/instrument (or combination) wins, but one announcement of "Cm" overcomes even the loudest of instruments. Then again, you may find that someone with a very different idea of what a specific chord should be has made an interesting contribution. If folks are just listening to your two notes and filling in the rest of the chord in their heads, it doesn't matter if they "hear" a different chord from the one you intended - they're going to imagine the one they like best.

Anecdote: I went to a harmony workshop with the group Artisan. They had the group sing Amazing Grace, but no one sang melody. Damned if it wasn't there anyway!