My apologies in advance if this is a stupid question, as I am not sure I entirely understand the mechanics(?) behind NBT, but is it possible to save an NBTTagCompound as a file on the client, rather than on the server?

Yes, the question is:

Why?

I am handling sensitive user data in a mod, and I am planning on adding encryption, and while I work on that, I was hoping perhaps I could store the data in an NBTTagCompound rather than the current format, a text file with a different extension, as a quick, temporary solution to users complaining about being able to read their information by opening the file in a text editor.

NBT files are not secure, by any means.

NBT files are not secure, by any means.

Oh trust me, I know, that is why I said as a temporary solution, meaning a day or two at most. I would still like to to this, as long as it isn't overly difficult to achieve, I don't want to spend a lot of time setting this up when I can be setting up actual security.

The answer to your question is "yes."  You just have to be aware that you're on the client side, not the server side.  If the data is on the server, you'll need to transmit it with packets.

Furthermore Minecraft is just Java so you can do regular Java file access stuff. There is a class called ByteBufUtils which has methods to easily write NBT to a buffer that you can then put into or out of a file stream.