Yes, I do depending on the design of the ring. I don't know where you live, but I know that in some countries either ring finger means engaged. My two cousins wear their wedding bands on their right. Also, recently I met a woman that had her engagement ring on her right ring finger. It's common, so most of the time I assume they are and don't bother with them.
Engagement rings are notably worn on the LEFT hand side to avoid confusion :P but some guys and people in general just see a ring and make assumptions without looking for the correct side. Technically, you shouldn't worry but because of these assumptions you may want to consider having it altered to fit another finger.