If the bottom is soft they will hold in a moderate to fast current. If the current really gets moving or grass and other debris gets caught on the lines, they will not hold well. I have spent a lot of time chasing dekes in moving water with those anchors.
Now, some of that was due to debris and another time it was due to my lines being too short to accommodate for the rise in tide. The lines have been taken care of, so tide height hasn't been an issue, but debris will always be something to watch out for. That is likely the case with any anchor though.