As with many "How come I can't ______?" sort of questions, the answer is "Security." And the short answer to your question is "no." The File System API was specifically designed solely as a method for web clients (e.g., browsers) to give developers a file system-like storage structure only through the API not from the outside.
Section "4.3 Security Considerations" of the API specification addresses exactly the behavior you're attempting. If the client were to store the raw files with their actual file names (e.g., "FinanceReport.doc") then it would make things much easier for malicious software on a compromised machine to locate and exploit sensitive data stored through the File System API. Also, if the actual file name were used, then it could make those files executable, such as storing "EvilActions.exe" on the local file system with that name. (Note: Some clients, such as Chrome, won't even let you store executables.) These are some of the reasons you see the obfuscation of file and storage. In fact, the API does not explicitly specify how the client should store the data, only that local storage raises security concerns that clients should address.
I recently completed a full scale security assessment of HTML5, including the File System API. I assure you that as the API and client implementation if the API both mature, you will almost certainly see further measures to block or at least obfuscate locally stored data vis-a-vis access from outside the client. To further bolster local storage security, clients may even shift toward storing the whole thing as one big file, similar to how MS Access uses a .mdb
file for storage. Again, it's entirely up to the client. Because you're attempting a sort of backdoor access to the data/files apart from the API, and doing so in an manner specifically called out as a "security concern" in the API, it's likely that any "solution" you employ today may fail tomorrow as client security matures. If you can do it for legitimate purposes, malware authors can do is for malicious purposes, and client manufacturers will do what they can to prevent that.