As it stands, no, there's no direct serving of files off of cloud storage via Subsonic. Everything Subsonic sees has to be on a locally accessed filesystem "mounted" on the computer. Generally if you can see it in Finder / Explorer, then Subsonic can reference it.
There are some applications/drivers for Windows and OSX that can mount some cloud drives onto your file system. E.g., I know of at least 2 that can do that for Amazon-hosted S3 databases. For HiDrive, it *may* work.
https://www.free-hidrive.com/faq/ - click "How can I set up my HiDrive account as a drive on my computer?" and be sure to specify a drive letter. Then you can add that path to your Subsonic server (assuming you're running on windows - it doesn't give instructions for setting it up for Linux or OSX) and it should find it. However, that windows drive feature appears to only work when you have a paid plan (the 5.80 or higher per month fee).
Some cloud services cost money for traffic, and it should be noted that the initial scan will look at EVERY file, so a large collection is going to be a lot of bandwidth in a very short time. Also, regular usage will use surprisingly a lot more bandwidth than you might expect. I regularly have phone data usage in the multiple gigs, though for me and Sprint (US) that's free. HiDrive appears to have free traffic, so that's a plus there. Other cloud drive systems cost money when you pass a certain amount.
It won't serve directly from the cloud drive. Every file will be downloaded to your home server and then relayed back out again to your browser or device. If you have home bandwidth upload limits, that too is a concern to watch for.
So yeah, it can be done, but it isn't built-in, intuitive, nor without side effects in bandwidth that may affect you.