Hmmmm I think the answer is no, because if you get infected with say a cryptolocker it will encrypt all files and folders it can find, including the HDD or USB, the sandboxed version of it is basically to protect the rest of your computer if your HDD has malware and has begun encrypting. It will only encrypt within the sandbox and leave the rest of your computer alone.
Think of it like this, your real computer has run files X, Y and Z while inside your sandbox has fake copies that are called X', Y' and Z'. When you run a cryptolocker unsandboxed it will affect all unsandboxed files, meaning X, Y and Z. If you run it in a sandbox it will of course only affect the sandboxed files, X', Y' and Z'. Running your HDD in sandbox will only protect your computer from malware within the HDD because only the HDD is sandboxed. If you run a malware outside the sandbox and your HDD is plugged in, then the malware would encrypt all files, no matter in the sandbox or not.
What happens when you sandbox your HDD is that it makes a copy of the files into your sandbox folder, and temporarily stores it there until you close the session, in which all data is cleared.
I hope you understand my long explanation