Yes you can do this if you have a system where both the src files are accessible and the NAS. There are several ways to do this with a single command, but the tool
rsync is probably the best one to go with:
$ sudo rsync -avz src /mnt/NAS/
-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)
-v, --verbose increase verbosity
-z, --compress compress file data during the transfer
-a switch is actually a macro for a whole bunt of switches:
-r, --recursive recurse into directories
-l, --links copy symlinks as symlinks
-p, --perms preserve permissions
-t, --times preserve modification times
-g, --group preserve group
-o, --owner preserve owner (super-user only)
-D same as --devices --specials
Running as root
You'll want to run this as root to preserve the permissions and ownerships of the files + directories. Also this particular root user will need access to the NAS. This is sometimes not setup by default so you may need the help of an admin if you're not the one.
Before you get started
Typically you'll want to do some upfront analysis on the directories in question to see if there are any symbolic links or fifo type files. These will require additional switches to
rsync so that it recreates them correctly in the target directory.
No direct mounting access to NAS
All is not lost if you can't directly mount the NAS on the same box where you have access to the src files. You can also
$ sudo rsync -avz src root@remoteserver:/mnt/NAS/.
There are more advanced options if neither of these suite your needs.