The Simple answer is yes what you want to-do can be done, BUT it will depend on some of the kit,as Him Her mentioed you cannot run a VPN connection between your device (outside) and the home router.
It does however as you say FTP sound like you can use this to move files, however your outside device would need to be able to use FTP.
you will need to make sure the FTP username and password you use are VERY secure as you will basically be opening this service up to the entire internet, the username and password are going to be the ONLY thing stopping hackers / automated scripts from getting access to your files from your NAS.
I would suggest as Him Her mentions, setup the FTP service internally (just accessible within your home) and play around with it make sure its going to-do what you want it to before wasting time with getting it working outside your home.
once your confident it works and does what you need it to make sure you set a strong username and password (google will give best advice on how to pick one). then set your router setup to port foward the Nas's FTP service to the internet (again google will have good advice on this and sometimes your provider will also help out).
then test it outside from work, or your mobile (switch wifi off of course).
for reference I've got 14 years of working in IT behind me if you need any other IT help, its a blessing and a curse lol
let us know how you get on.
