Bittorrent Sync is now Resilio Sync, and it's in fact accessible.
https://www.resilio.com/individuals/
Resilio Sync has a web interface supporting all modern web browser, so it's possible to use it with NVDA and Jaws.
However, in order to set up Resilio Sync you must start the app with a commandline switch /webui.
Instructions for Windows:
1. Install Resillio Sync.
2. Locate the app short i the start menu.
3. Change the properties for the program launch by adding /webui to the program path and launch the app from the Start Menu.
Then the startup wizard opens in the default web browser and the remaining process is very accessible.
I can't help with MacOSX or Linux, but I assume that the steps are similar.