No, it's not safe to use those tools while the directory is updating. They all traverse the directory and will copy the contents of the file at the point they happen to check it, and will not check again later (and, even if they did, there's still a race-condition there).
An LVM snapshot (or simply pausing the processes that touch those files) would be an appropriate solution.
An alternative solution would be to use lsyncd or SyncThing, or some other tool that continuously watches for changes.