Renaming a file normally won't interfere with running but it will only use the new file on reboot.
It should take no bandwidth and less than a minute to synchronize all your files if they have already been copied. (assuming it stores the hashed state like normal bittorrent, or uses rsync tricks)
WARNING: Bittorrent Sync is not open source and not fully distributed so it may become unusable in the future. There are more flexible options (rsync, git-annex, etc).
(rsync will verify/sync 15TB in under a minute on a raspberrypi)
If Bittorrent Sync is running you will see it in
ps ax | grep -i sync and you can safely ask it to stop with
kill $PID (or if it won't stop, you can use
kill -9 $PID to force stop it).
It may not have been installed with it's own service but instead might be in
grep -i sync /etc/init.d/rc.local or
crontab -l | grep -i sync or other less savory places.
It's good practice to keep an install.log on servers to let future admins know what (and how) was changed from the default distribution.