My question is: can I still fall or turn over my foot when I have the brace on?
Falling is definitely a possibility. But I'm with fast_clay...play with two if you can...but get some good physical therapy routines and work on regaining both strength and flexibility as soon as you can without re-injury. Don't come to rely on the brace to make up for sloppy footwork.
I tore my ankle up years ago playing volleyball and it took a full year to get back to "normal." The Fear, however, of turning it over again...still lives on.