It is definitely not appropriate. If you break the chop sticks and use them correctly your fingers will never touch the surface where there are splinters.
I always do it under the table; something I instinctively do without ever being told to. Now I wonder if I might have picked up on nonverbal cues at some point in the past. If I were someplace where chopsticks were the norm, I would probably just carry my own as I find the disposable wooden ones very off putting. I have to wonder if there is a rule about using your own chopsticks though.
It is definitely not appropriate. If you break the chop sticks and use them correctly your fingers will never touch the surface where there are splinters.