Yes. You can put a trap into the path of a monster and you won't be detected (assuming you wouldn't just be detected normally). You can also have that trap blow up on them, and they won't be any the wiser. They might do a search check, but that's about it.
One clever thing I discovered is that you can combine a noise maker and a mine. First you place the mine down, then the noisemaker, and back away. The noisemaker will go off, luring the monster to the trap. It's really great for those monsters that don't have patrol patterns and just stay still.
I tried to lay out a trail of noisemakers, but that has turned out to be ineffective if not impossible. The noisemakers don't last long enough, and the cooldown is too long on mines to be able to set up another one in time to continually grab attention. Maybe this is different for some monsters, but the kobolds I was testing on like to return to their home positions quickly after investigating a noise.