Can ornate box turtles swim

I believe the turtle floats-being guided by his legs...however he may dive and remain stationary on the bottom of the water he is in for a proscribed amount of time

Sure they can swim but nowhere near as good as an aquatic turtle so they avoid fast moving bodies of water and usually will not venture in deeper than the height of their shell - they seem to know they can be swept away. Often when they are sick they will seek water to soak in and often will die soaking in the water.