It is most definitely possible to do what you suggest and encrypt the NASLite file system. It will probably work well, but security, like everything else comes with added responsibility and some system overhead. Here are some things to consider:
1. If you forget or loose the filesystem password, you just lost your data.
2. If something goes wrong and the filesystem brakes, you just lost your data.
3. The server OS will have to encrypt and decrypt on the fly, so less capable machines will probably not offer the necessary performance.
4. Rebooting the server will require that you log-in to “unlock” the filesystems, making recovery due to unexpected reboots (power failure, etc) impossible.
It also seems out of context given the light-weight, open nature of the NASLite products. Perhaps, a different product may target that functionality, with some form of user management that will be necessary.
Just my thoughts