Yes, there is a cutout in the case that makes the USB port accessible. You can access the wifi button as well. However, you must remove the camera from the case if you want to take out the MicroSD card.
I have this skeleton case and it works fine. The mini usb end of the charging cord easily plugs in, and all of the buttons are fully accessible. Maybe the end of the plug was slightly damaged, and is why you needed to file it down?
The Hero 3 and 3+ cameras are physically identical.
The 3+ comes with a slimmer "hard case" housing that GoPro bills as "30% smaller and lighter", but the camera inside it is exactly the same shape and size.
It kind of fits and what I mean by that is the button wholes are too small which keep the buttons presses and render then camera useless. So You have to drill the holes a little bigger or slip a small cardboard between the frame and the camera so the frame is not pressing down on the buttons. I used a sand paper to make the holes a little wider after that it works. (Hero 4 black)