From what I've seen most people either do both or none, although not many people wear suits around here, except during Spring Festival. Some wear blazers though.
Your gonna use a retailer's website where buttoning up the suit makes it look more presentable to people looking to purchase, that is clearly a selling-point on their part. I only see those who are ill informed actually button both buttons
I went to REI to buy some last-minute stuff for my trip to China. I made sure to buy hiking socks whose colors matched the shorts and casual pants I plan on wearing. I'm the only one who's going to notice, but that's all that matters.