I wonder if I can use Azure Blob Storage to store Mac Time Machine files. Is it really possible to mount a blob storage as a drive for Mac Time Machine?
Of course it's possible (possible as in it's doable, not possible as in "download, install and you are done). It's possible to write Mac OS X driver (for example using fuse) that mounts Blob Storage as local drive and then emulates HFS to Mac OS X. However, in practice that's really hard task.
So in short: no, it's not.
You may have better luck with installing netatalk (and AFP) with Time Capsule emulation, and then mount Blob Storage to Linux server. That way Mac OS X just thinks there is some storage, not actual HFS volume (and it'll create