Yes he can.
It's easiest done from a Walk. If you are walking at the fastest pace and tap back for 1 frame, you will carry your momentum during Turn for 17 frames. The first 10 frames or so are what count though. So that's pretty much your window. You have to tap back for only 1 frame though, if you do it for 2 frames, you will start a dash and will only carry momentum for 2 frames, it's still possible but it's unnecessary hard.
If you do it from a Dash, and tap back for just 1 frame, you carry momentum for 5 frames, but the distance is very small. If you tap back for longer then a frame, you will, like with a Walk, only carry momentum for 2 frames.
You cannot do this from a Run, as when you press back during a Run you start a TurnRun. No matter how close you are to the edge, you will never slide off. It is programmed into the game to stop your forward momentum when you reach it. This makes TurnRun much "faster" when done at the ledge. It doesn't decrease the amount of frames the animation takes, but it starts your backwards momentum the frame after you reach the edge. A regular TurnRun won't start moving backwards until frame 20 and you can see by the following Run animation how little momentum you have. A perfect TurnRun at an edge will start your backwards momentum on frame 2 and the following Run will be at fullspeed (1.02X value per frame) when it starts.
Now that I think about it, those carried momentum windows don't mean anything if you don't know the distance they go.
So I measured them by Battlefield Platform Dots
Fastest Walk > Turn (1-frame)
8 dots
Fastest Walk > Turn (2+ frames)
1.5 dots
Dash > Turn (1-frame)
1.2 dots
Dash > Turn (2+ frames)
0.7 dots
You can only slide off on the the 2nd frame or later of each window. So when you Turn for 2+ frames, you really only have 1 frame that can slide off.